Question:
Let $f: R \rightarrow R$ be a differentiable function such that its derivative $f^{\prime}$ is continuous and $f(\pi)=-6$. If $F$ : $[0$, $\pi] \rightarrow R$ is defined by $F(x)=\int\limits_{0}^{x} f(t) d t$, and if
$\int\limits_{0}^{\pi}\left(f^{\prime}(x)+F(x)\right) \cos x d x=2$
then the value of $f (0)$ is _____
Let $f: R \rightarrow R$ be a differentiable function such that its derivative $f^{\prime}$ is continuous and $f(\pi)=-6$. If $F$ : $[0$, $\pi] \rightarrow R$ is defined by $F(x)=\int\limits_{0}^{x} f(t) d t$, and if
$\int\limits_{0}^{\pi}\left(f^{\prime}(x)+F(x)\right) \cos x d x=2$
then the value of $f (0)$ is _____
$\int\limits_{0}^{\pi}\left(f^{\prime}(x)+F(x)\right) \cos x d x=2$
then the value of $f (0)$ is _____
Updated On: Apr 25, 2024
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Correct Answer: 4
Solution and Explanation
\(f(0)=4.\)
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