Question

\(\int_{-1}^1 \sin x \cos^3 x \, dx \)

• A. 2
• B. 1
• C. 0
• D. -1

Hint:

For integrals of odd functions over symmetric intervals, the result is always zero.

Answer 1

The Correct Option is C

We are given: \[ I = \int_{-1}^1 \sin x \cos^3 x \, dx \] The integrand is an odd function because \( \sin x \) is odd and \( \cos^3 x \) is even. The product of an odd function and an even function is odd, and the integral of an odd function over a symmetric interval \( [-1, 1] \) is zero. Thus, the correct answer is \( 0 \).