NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.1
Page No 299:
Question 1:
sin 2x
Answer:
The anti derivative of sin 2x is a function of x whose derivative is sin 2x.
It is known that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7381/NCERT_Solution_Math_Chapter_7_final_html_m697e7f3e.gif)
Therefore, the anti derivative of![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7381/NCERT_Solution_Math_Chapter_7_final_html_48bff6fa.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7381/NCERT_Solution_Math_Chapter_7_final_html_48bff6fa.gif)
Question 2:
Cos 3x
Answer:
The anti derivative of cos 3x is a function of x whose derivative is cos 3x.
It is known that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7383/NCERT_Solution_Math_Chapter_7_final_html_37502309.gif)
Therefore, the anti derivative of
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7383/NCERT_Solution_Math_Chapter_7_final_html_f130360.gif)
Question 3:
e2x
Answer:
The anti derivative of e2x is the function of x whose derivative is e2x.
It is known that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7385/NCERT_Solution_Math_Chapter_7_final_html_m28a7365e.gif)
Therefore, the anti derivative of
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7385/NCERT_Solution_Math_Chapter_7_final_html_574470f7.gif)
Question 4:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7386/NCERT_Solution_Math_Chapter_7_final_html_d228bea.gif)
Answer:
The anti derivative of
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7386/NCERT_Solution_Math_Chapter_7_final_html_d228bea.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7386/NCERT_Solution_Math_Chapter_7_final_html_d228bea.gif)
It is known that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7386/NCERT_Solution_Math_Chapter_7_final_html_m22680595.gif)
Therefore, the anti derivative of
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7386/NCERT_Solution_Math_Chapter_7_final_html_m55fbb48.gif)
Question 5:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_m64ac22d.gif)
Answer:
The anti derivative of
is the function of x whose derivative is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_m77e75aff.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_m77e75aff.gif)
It is known that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_37d39277.gif)
Therefore, the anti derivative of
is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_m77e75aff.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7387/NCERT_Solution_Math_Chapter_7_final_html_7e5b283f.gif)
Question 6:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7388/NCERT_Solution_Math_Chapter_7_final_html_m1fde19c0.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7388/NCERT_Solution_Math_Chapter_7_final_html_m1fde19c0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7388/NCERT_Solution_Math_Chapter_7_final_html_55f021fe.gif)
Question 7:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7389/NCERT_Solution_Math_Chapter_7_final_html_76cc6ec4.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7389/NCERT_Solution_Math_Chapter_7_final_html_76cc6ec4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7389/NCERT_Solution_Math_Chapter_7_final_html_5e8acc03.gif)
Question 8:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7390/NCERT_Solution_Math_Chapter_7_final_html_5ebb449b.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7390/NCERT_Solution_Math_Chapter_7_final_html_5ebb449b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7390/NCERT_Solution_Math_Chapter_7_final_html_146e5d64.gif)
Question 9:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7391/NCERT_Solution_Math_Chapter_7_final_html_4b2d046b.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7391/NCERT_Solution_Math_Chapter_7_final_html_4b2d046b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7391/NCERT_Solution_Math_Chapter_7_final_html_1319c4b3.gif)
Question 10:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7392/NCERT_Solution_Math_Chapter_7_final_html_m21b097a0.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7392/NCERT_Solution_Math_Chapter_7_final_html_m21b097a0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7392/NCERT_Solution_Math_Chapter_7_final_html_353d003.gif)
Question 11:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7393/NCERT_Solution_Math_Chapter_7_final_html_m45687b1f.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7393/NCERT_Solution_Math_Chapter_7_final_html_m45687b1f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7393/NCERT_Solution_Math_Chapter_7_final_html_m60c06e96.gif)
Question 12:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7394/NCERT_Solution_Math_Chapter_7_final_html_m352a7734.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7394/NCERT_Solution_Math_Chapter_7_final_html_m352a7734.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7394/NCERT_Solution_Math_Chapter_7_final_html_75ad4a9d.gif)
Question 13:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7395/NCERT_Solution_Math_Chapter_7_final_html_m762c7093.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7395/NCERT_Solution_Math_Chapter_7_final_html_m762c7093.gif)
On dividing, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7395/NCERT_Solution_Math_Chapter_7_final_html_19f077a8.gif)
Question 14:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7396/NCERT_Solution_Math_Chapter_7_final_html_1b1677ba.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7396/NCERT_Solution_Math_Chapter_7_final_html_1b1677ba.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7396/NCERT_Solution_Math_Chapter_7_final_html_982111b.gif)
Question 15:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7397/NCERT_Solution_Math_Chapter_7_final_html_ef118c8.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7397/NCERT_Solution_Math_Chapter_7_final_html_ef118c8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7397/NCERT_Solution_Math_Chapter_7_final_html_2b7fadb0.gif)
Question 16:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7398/NCERT_Solution_Math_Chapter_7_final_html_70eedab9.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7398/NCERT_Solution_Math_Chapter_7_final_html_70eedab9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7398/NCERT_Solution_Math_Chapter_7_final_html_m155aa073.gif)
Question 17:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7399/NCERT_Solution_Math_Chapter_7_final_html_m3513f78e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7399/NCERT_Solution_Math_Chapter_7_final_html_m3513f78e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7399/NCERT_Solution_Math_Chapter_7_final_html_552b2cfe.gif)
Question 18:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7400/NCERT_Solution_Math_Chapter_7_final_html_55f8b69e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7400/NCERT_Solution_Math_Chapter_7_final_html_55f8b69e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7400/NCERT_Solution_Math_Chapter_7_final_html_m6170702b.gif)
Question 19:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7401/NCERT_Solution_Math_Chapter_7_final_html_69cfa7d9.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7401/NCERT_Solution_Math_Chapter_7_final_html_m5d1cbb50.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7401/NCERT_Solution_Math_Chapter_7_final_html_m8779d63.gif)
Question 20:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7402/NCERT_Solution_Math_Chapter_7_final_html_m4223465.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7402/NCERT_Solution_Math_Chapter_7_final_html_m4223465.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7402/NCERT_Solution_Math_Chapter_7_final_html_m63d2802c.gif)
Question 21:
The anti derivative of
equals
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_a26abdd.gif)
(A)
(B) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_ma784259.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_m2e4ffec8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_ma784259.gif)
(C)
(D) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_5e1b84c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_m69b8925b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_5e1b84c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_m53d4ecad.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7403/NCERT_Solution_Math_Chapter_7_final_html_7839ddd7.gif)
Hence, the correct answer is C.
Question 22:
If
such that f(2) = 0, then f(x) is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_3ad53d45.gif)
(A)
(B) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_b8a8947.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m5b7aba32.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_b8a8947.gif)
(C)
(D) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m36086418.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_503df879.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m36086418.gif)
Answer:
It is given that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_3ad53d45.gif)
∴Anti derivative of ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_58a9a3ab.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_58a9a3ab.gif)
∴![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m38dfbbfb.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m38dfbbfb.gif)
Also,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7404/NCERT_Solution_Math_Chapter_7_final_html_m601912de.gif)
Hence, the correct answer is A.