Question:
Let f : [0, π] → \(\R\) be the function defined by
\(f(x)=\begin{cases} (x-\pi)e^{\sin x} & \text{if } 0 \le x \le \frac{\pi}{2},\\ xe^{\sin x}+\frac{4}{\pi} & \text{if }\frac{\pi}{2}\lt x \le \pi. \end{cases}\)
Then the value of
\(\int\limits_0^{\pi}f(x)dx\)
is equal to _________. (Rounded off to two decimal places)
Let f : [0, π] → \(\R\) be the function defined by
\(f(x)=\begin{cases} (x-\pi)e^{\sin x} & \text{if } 0 \le x \le \frac{\pi}{2},\\ xe^{\sin x}+\frac{4}{\pi} & \text{if }\frac{\pi}{2}\lt x \le \pi. \end{cases}\)
Then the value of
\(\int\limits_0^{\pi}f(x)dx\)
is equal to _________. (Rounded off to two decimal places)
\(f(x)=\begin{cases} (x-\pi)e^{\sin x} & \text{if } 0 \le x \le \frac{\pi}{2},\\ xe^{\sin x}+\frac{4}{\pi} & \text{if }\frac{\pi}{2}\lt x \le \pi. \end{cases}\)
Then the value of
\(\int\limits_0^{\pi}f(x)dx\)
is equal to _________. (Rounded off to two decimal places)
Updated On: Oct 1, 2024
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Correct Answer: 2
Solution and Explanation
The correct answer is : 2.
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