Question

Evaluate: \[ \int_{\pi/4}^{5\pi/4} \left(\cos t |\sin t| + \sin t |\cos t|\right) dt = \]

• A. 0
• B. 1
• C. \( \frac{1}{2} \)
• D. \( \frac{\sqrt{3}}{2} \)

Hint:

Check for symmetry or odd/even nature of functions to evaluate definite integrals quickly.

Answer 1

The Correct Option is A

Break the integral into regions where \( \sin t \) and \( \cos t \) are positive/negative. The function is odd and symmetric about \( \pi \), so integral over symmetric interval results in zero.