Topic: Engineering Mathematics
$\int_{0}^{\pi/2}\sin^{7}x~dx~is$
- A. $\frac{8}{35}$
- B. $\frac{16}{35}$
- C. 0
- D. 1
Answer: B. $\frac{16}{35}$
Explanation: Using Wallis' formula for definite integrals of the form $\int_{0}^{\pi/2}\sin^{n}x~dx$, when n is an odd integer: $\frac{n-1}{n} \times \frac{n-3}{n-2} \times \dots \times \frac{2}{3} \times 1$. For $n=7$, the integral is $\frac{6}{7} \times \frac{4}{5} \times \frac{2}{3} = \frac{48}{105} = \frac{16}{35}$.