Use differentiation to determine whether the integral formula is correct.
-$$\int x \sin x d x = - x \cos x + \sin x + C$$

Question

Quizplus · Accepted Answer

We can differentiate the given integral formula to check if it is correct:

\begin{align*}
\frac{d}{dx}\left[-x\cos x + \sin x + Cight] &= -\frac{d}{dx}x\cos x + \frac{d}{dx}\sin x + \frac{d}{dx}C\
&= -\cos x + x\sin x + 0\
&= x\sin x - \cos x
\end{align*}

This matches the integrand, so the integral formula is correct.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫xsin⁡xdx=−xcos⁡x+sin⁡x+C\int x \sin x d x = - x \cos x + \sin x + C∫xsinxdx=−xcosx+sinx+C

Use Differentiation to Determine Whether the Integral Formula Is Correct $\int x \sin x d x = - x \cos x + \sin x + C$