If \(f(x) = \begin{cases} e^{\sin x} & \text{for } |x| \leq \pi/2 \\ 2 & \text{otherwise} \end{cases}\) , then \(\int_{-\pi}^{\pi} \frac{2f(x)}{\cos x} dx\) is

Definite Integration

Integrals of Piecewise Functions

Grade 12

Question:

If \(f(x) = \begin{cases} e^{\sin x} & \text{for } |x| \leq \pi/2 \\ 2 & \text{otherwise} \end{cases}\), then \(\int_{-\pi}^{\pi} \frac{2f(x)}{\cos x} dx\) is

(A) 0

(B) 1

(C) 2

(D) 3

Step-by-Step Solution

Key Concept: Analyze the piecewise function and recognize that the integrand may be odd or even on the symmetric interval.

IIT - 2000

Correct Answer: A

Question:

Step-by-Step Solution

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