Question

\(\displaystyle \int_{-1}^{1}\sin^{17}x\,\cos^{3}x\,dx=\) ?

• A. \(\dfrac{12}{5}\)
• B. \(0\)
• C. \(1\)
• D. \(\dfrac{3}{5}\)

Hint:

Check $f(-x)$; odd functions vanish on symmetric limits.

Answer 1

The Correct Option is B

Parity: \(\sin^{17}x\) is odd, \(\cos^{3}x\) is even. Odd\(\times\)even \(=\) odd. Integral of an odd function over \([-a,a]\) is \(0\). Limits \([-1,1]\) are symmetric, so integral \(=0\).