# CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(l)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(l) Textbook Exercise questions and Answers.

## CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(l)

Question 1.
$$\int_0^{\frac{\pi}{2}}$$sin10 θ dθ
Solution:
$$\int_0^{\frac{\pi}{2}}$$sin10 θ dθ = $$\frac{9}{10} \cdot \frac{7}{8} \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi}{2}$$ = $$\frac{405 \pi}{7680}$$

Question 2.
$$\int_0^{\frac{\pi}{2}}$$cos12 θ dθ
Solution:
$$\int_0^{\frac{\pi}{2}}$$cos12 θ dθ = $$\frac{11}{12} \cdot \frac{9}{10} \cdot \frac{7}{8} \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi}{2}$$ = $$\frac{4455 \pi}{92160}$$

Question 3.
$$\int_0^{\frac{\pi}{2}}$$sin11 θ dθ
Solution:
$$\int_0^{\frac{\pi}{2}}$$sin11 θ dθ = $$\frac{10}{11} \cdot \frac{8}{9} \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}$$ = $$\frac{3840}{4455}$$

Question 4.
$$\int_0^{\frac{\pi}{2}}$$cos9 θ dθ
Solution:
$$\int_0^{\frac{\pi}{2}}$$cos9 θ dθ = $$\frac{8}{9} \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}$$ = $$\frac{384}{405}$$

Question 5.
$$\int_0^1 \frac{x^7}{\sqrt{1-x^2}}$$ dx
Solution:

Question 6.
$$\int_0^1 \frac{x^5\left(4-x^2\right)}{\sqrt{1-x^2}}$$ dx
Solution:

Question 7.
$$\int_0^a x^3\left(a^2-x^2\right)^{\frac{5}{2}}$$ dx
Solution:

Question 8.
$$\int_0^1 x^5 \sqrt{\frac{1+x^2}{1-x^2}}$$ dx
Solution:

Question 9.
$$\int_0^{\infty} \frac{x^2}{\left(1+x^6\right)^n}$$ dx
Solution:

Question 10.
$$\int_0^\pi$$sin8 θ dθ
Solution: