Question

The value of \( \int_0^{\frac{\pi}{2}} e^x \cos x \, dx \) is equal to:

• A. \( \frac{1}{2} (e - 1) \)
• B. \( \frac{1}{2} (e^x - 1) \)
• C. \( \frac{1}{2} (e^{\pi/2} - 1) \)
• D. \( \frac{1}{2} (1 - e^{\pi/2}) \)

Hint:

Remember to apply integration by parts to solve integrals involving products of exponential and trigonometric functions.

Answer 1

The Correct Option is C

Using integration by parts, the result of the integral is \( \frac{1}{2} \left( e^{\pi/2} - 1 \right) \).