Reduction formulae Quiz

1. What is $I_0=\int_0^{\frac{\pi}{2}}\sin^0x\,dx$?

• A. $\frac{\pi}{2}$
• B. $1$
• C. $0$
• D. $\pi$

2. Given $nI_n=(n-1)I_{n-2}$, which expression gives $I_7$ in terms of $I_5$?

• A. $\frac76I_5$
• B. $\frac56I_5$
• C. $\frac67I_5$
• D. $\frac{7}{5}I_5$

3. Find the exact value of $I_4$.

• A. $\frac{3\pi}{8}$
• B. $\frac{3\pi}{16}$
• C. $\frac34$
• D. $\frac{3\pi}{32}$

4. In the derivation, $\left[-\sin^{n-1}x\cos x\right]_0^{\frac{\pi}{2}}$ equals

• A. $1$
• B. $-1$
• C. $n-1$
• D. $0$

5. Which expression equals $\sin(n+2)x-\sin nx$?

• A. $2\cos(n+1)x\sin x$
• B. $2\sin(n+1)x\cos x$
• C. $2\cos(n+1)x\cos x$
• D. $\sin2x$