NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.9
Page No 338:
Question 1:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7742/NCERT_Solution_Math_Chapter_7_final_html_m1067703e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7742/NCERT_Solution_Math_Chapter_7_final_html_39473b81.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7742/NCERT_Solution_Math_Chapter_7_final_html_m5b213be6.gif)
Question 2:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7743/NCERT_Solution_Math_Chapter_7_final_html_480f9557.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7743/NCERT_Solution_Math_Chapter_7_final_html_51690e6.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7743/NCERT_Solution_Math_Chapter_7_final_html_303663d0.gif)
Question 3:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7745/NCERT_Solution_Math_Chapter_7_final_html_m70152f9b.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7745/NCERT_Solution_Math_Chapter_7_final_html_m20e8f6a9.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7745/NCERT_Solution_Math_Chapter_7_final_html_m35238a09.gif)
Question 4:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7746/NCERT_Solution_Math_Chapter_7_final_html_4ba6d54a.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7746/NCERT_Solution_Math_Chapter_7_final_html_m2e6c9f5f.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7746/NCERT_Solution_Math_Chapter_7_final_html_6256f83d.gif)
Question 5:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7747/Items%20179_html_1c52a724.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7747/Items%20179_html_608a452e.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7747/Items%20179_html_m3cd3c92d.gif)
Question 6:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7749/NCERT_Solution_Math_Chapter_7_final_html_426fe2e4.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7749/NCERT_Solution_Math_Chapter_7_final_html_m5c2222aa.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7749/NCERT_Solution_Math_Chapter_7_final_html_m6026a9a1.gif)
Question 7:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7751/NCERT_Solution_Math_Chapter_7_final_html_m38d7921f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7751/NCERT_Solution_Math_Chapter_7_final_html_m4d2e837b.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7751/NCERT_Solution_Math_Chapter_7_final_html_m44340047.gif)
Question 8:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7752/NCERT_Solution_Math_Chapter_7_final_html_m1498ff3f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7752/NCERT_Solution_Math_Chapter_7_final_html_m6da61a7.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7752/NCERT_Solution_Math_Chapter_7_final_html_m7c581a2d.gif)
Question 9:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7754/NCERT_Solution_Math_Chapter_7_final_html_m166e5b62.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7754/NCERT_Solution_Math_Chapter_7_final_html_m2b080397.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7754/NCERT_Solution_Math_Chapter_7_final_html_14d81098.gif)
Question 10:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7756/NCERT_Solution_Math_Chapter_7_final_html_m81460a9.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7756/NCERT_Solution_Math_Chapter_7_final_html_m4f2ac16.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7756/NCERT_Solution_Math_Chapter_7_final_html_m2c4074b2.gif)
Question 11:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7760/NCERT_Solution_Math_Chapter_7_final_html_682faf17.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7760/NCERT_Solution_Math_Chapter_7_final_html_61f2f3f1.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7760/NCERT_Solution_Math_Chapter_7_final_html_m2f2f6fbd.gif)
Question 12:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7762/Item%20186_html_407b64a3.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7762/Item%20186_html_7c21c7f5.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7762/Item%20186_html_m19730f06.gif)
Question 13:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7763/NCERT_Solution_Math_Chapter_7_final_html_79211595.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7763/NCERT_Solution_Math_Chapter_7_final_html_m9bd612c.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7763/NCERT_Solution_Math_Chapter_7_final_html_m45040b1.gif)
Question 14:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7764/NCERT_Solution_Math_Chapter_7_final_html_1c0733f6.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7764/NCERT_Solution_Math_Chapter_7_final_html_7b54546e.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7764/NCERT_Solution_Math_Chapter_7_final_html_mebefe21.gif)
Question 15:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7765/NCERT_Solution_Math_Chapter_7_final_html_6d91cb30.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7765/NCERT_Solution_Math_Chapter_7_final_html_m6ca16809.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7765/NCERT_Solution_Math_Chapter_7_final_html_m2160b3b9.gif)
Question 16:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_1a209d0c.gif)
Answer:
Let ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_ma123791.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_ma123791.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_m3e58e905.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_2453d8c5.gif)
Equating the coefficients of x and constant term, we obtain
A = 10 and B = −25
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_91e9a9d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_90155e9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_m9471e1f.gif)
Substituting the value of I1 in (1), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7766/NCERT_Solution_Math_Chapter_7_final_html_m6af71c41.gif)
Question 17:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7767/NCERT_Solution_Math_Chapter_7_final_html_62748c4f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7767/NCERT_Solution_Math_Chapter_7_final_html_799ad7cb.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7767/NCERT_Solution_Math_Chapter_7_final_html_m160b5348.gif)
Question 18:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7769/Item%20192_html_m1a378172.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7769/Item%20192_html_3225002c.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7769/Item%20192_html_m58ae84a8.gif)
Question 19:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7771/Item%20193_html_24e76ff5.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7771/Item%20193_html_6ea94b8.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7771/Item%20193_html_17842141.gif)
Question 20:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7774/Item%20194_html_m53e235e1.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7774/Item%20194_html_662f5233.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7774/Item%20194_html_1dd66a6f.gif)
Question 21:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_14e7e996.gif)
A. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m4e8d241e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m4e8d241e.gif)
B. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_552167fc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_552167fc.gif)
C. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m217ed0f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m217ed0f1.gif)
D. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m2fcd969f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m2fcd969f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m4a2a6a82.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7777/NCERT_Solution_Math_Chapter_7_final_html_m6107f62f.gif)
Hence, the correct answer is D.
Question 22:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m45705453.gif)
A. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m217ed0f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m217ed0f1.gif)
B. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m2fcd969f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m2fcd969f.gif)
C. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m4b3990c3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m4b3990c3.gif)
D. ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m6201c3cd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_m6201c3cd.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_39a413bc.gif)
By second fundamental theorem of calculus, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7780/Item%20196_html_3ccb1065.gif)
Hence, the correct answer is C.