alleryIf $\displaystyle f(x) = \int_0^x t \sin t\, dt$, then $f''(\pi) = ?$
A$-\pi$
B$\pi$
C$0$
D$1$
Answer & Solution
Correct answer: A. $-\pi$
By FTC, $f'(x) = x\sin x$.
**Differentiating:** $f''(x) = \sin x + x\cos x$.
At $x = \pi$: $f''(\pi) = \sin\pi + \pi\cos\pi = 0 + \pi(-1) = -\pi$.
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