Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.3

Find the integrals of the following:

Question 1.

sin^{2}(2x + 5)

Solution:

Question 2.

sin3x cos4x

Solution:

Question 3.

cos2x cos4x cos6x

Solution:

Question 4.

sin^{3}(2x + 1)

Solution:

Question 5.

sin^{3}x cos^{3}x

Solution:

Question 6.

sinx sin2x sin3x

Solution:

Question 7.

sin4x sin8x

Solution:

Question 8.

\(\frac{1-cosx}{1+cosx}\)

Solution:

Question 9.

\(\frac{cosx}{1+cosx}\)

Solution:

Question 10.

sin^{4}x

Solution:

Question 11.

cos^{4}2x

Solution:

Question 12.

\(\frac{\sin ^{2} x}{1+\cos x}\)

Solution:

= x – sinx + C.

Question 13.

\(\frac{cos2x-cos2α}{cosx-cosα}\)

Solution:

Question 14.

\(\frac{cosx-sinx}{1+sin2x}\)

Solution:

Question 15.

tan^{3}2x sec2x

Solution:

Question 16.

tan^{4}x

Solution:

Question 17.

\(\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}\)

Solution:

Question 18.

\(\frac{\cos 2 x+2 \sin ^{2} x}{\cos ^{2} x}\)

Solution:

Question 19.

\(\frac{1}{\sin x \cos ^{3} x}\)

Solution:

Question 20.

\(\frac{\cos 2 x}{(\cos x+\sin x)^{2}}\)

Solution:

Question 21.

sin^{-1}x

Solution:

Question 22.

\(\frac{1}{cos(x-a)cos(x-b)}\)

Solution:

Choose the correct answers in the following questions 23 and 24:

Question 23.

∫ \(\frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x}\)

(A) tan x + cot x + C

(B) tan x + cosec x + C

(C) – tan x + cot x + C

(D) tan x + sec x + C

Solution:

∴ part (A) is the correct answer.

Question 24.

∫ \(\frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)}\) is equal to.

(A) – cot (e.x^{x})

(B) tan (x.e^{x}) + C

(C) tan (e^{x}) + C

(D) cot (e^{x}) + C

Solution:

I = ∫ \(\frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)}\) dx.

Put x e^{x} = t, so that (e^{x} + x e^{x}) dx = dt.

or e^{x}(1 + x)dx = dt

∴ I = ∫ \(\frac{d t}{\cos ^{2} t}\) = ∫sec^{2} t dt = tan t + C.

= tan(x e^{x}) + C.

∴ Part (B) is the correct answer.