Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(h) Textbook Exercise questions and Answers.
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(h)
Evaluate the following Integrals.
Question 1.
(i) ∫\frac{d x}{4+5 \cos x}
Solution:
(ii) ∫\frac{d x}{3+\cos x}
Solution:
(iii) ∫\frac{d x}{3+\sin x}
Solution:
(iv) ∫\frac{d x}{1+2 \sin x}
Solution:
(v) ∫\frac{d x}{2 \sin x+3 \cos x}
Solution:
(vi) ∫\frac{d x}{1+\cos x+\sin x}
Solution:
Question 2.
(i) ∫\frac{3 \sin x+28 \cos x}{5 \sin x+6 \cos x} dx
Solution:
(ii) ∫\frac{12 \sin x-2 \cos x+3}{\sin x+\cos x} dx
Solution:
Let 12 sin x – 2 cos x = A (sin x + cos x) + B ( cos x – sin x)
[Note that cos x – sin x is the derivative of sin x + cos x]
Then A – B = 12, A + B = -2
⇒ 2A = 10
⇒ A = 5, B = -7
Thus 12 sin x – 2 cos x = 5 (sin x + cos x) – 7 (cos x – sin x)
(iii) ∫\frac{5 \sin x}{3-2 \sin x} dx
Solution:
(iv) ∫\frac{2 \cos x+7}{4-\sin x} dx
Solution:
Question 3.
(i) ∫\frac{d x}{2 \cos ^2 x+3 \cos x}
Solution:
(ii) ∫\frac{d x}{4 \sin ^2 x-\sin x}
Solution:
(iii) ∫\frac{\sin x \cos x}{x \sin ^2 x-2 \sin x+3} dx
Solution:
(iv) ∫\frac{d x}{\cos x-\cos 3 x}
Solution:
Question 4.
(i) ∫\frac{d \theta}{4+3 \sin ^2 \theta}
Solution:
(ii) ∫\frac{d \theta}{2-3 \cos ^2 \theta}
Solution:
(iii) ∫\frac{d \theta}{4 \cos ^2 \theta+9 \sin ^2 \theta}
Solution:
(iv) ∫\frac{d \theta}{2+3 \cos ^2 \theta-4 \sin ^2 \theta}
Solution:
Question 5.
(i) ∫\frac{\sin 3 x}{\cos 7 x \cos 4 x} dx
Solution:
(ii) ∫\frac{\cos 2 x}{\sin 7 x \cos 5 x} dx
Solution:
Question 6.
(i) ∫\frac{d x}{\cos x(5+3 \cos x)}
Solution:
(ii) ∫\frac{d x}{\cos x(1+2 \sin x)}
Solution:
