Let p=\int_{a}^{b}f(x)\,dx and q=\int_{a}^{b}|f(x)|\,dx. If f(x)=e^{-x}, then which one of the following is correct?

Explanation

For all real values of x, the exponential function e^{-x} is strictly positive. Therefore, |f(x)| = |e^{-x}| = e^{-x} = f(x). Since the integrand is identical, their definite integrals over [a, b] are exactly equal, meaning p = q.

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