Use differentiation to determine whether the integral formula is correct.
-$$\int x \cos x d x = \frac { x ^ { 2 } } { 2 } \sin x + C$$

Name: Use differentiation to determine whether the integral formula is correct. -\[\int x \cos x d x = \frac { x ^ { 2 } } { 2 } \sin x + C\]
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Question

Quizplus · Accepted Answer

If we differentiate the given formula, we get:
$$\frac{d}{dx}\left(\frac{x^2}{2}\sin x+C\right)=x\cos x+\frac{x}{2}\sin x$$
Which is not equal to the integrand $x\cos x$. Therefore, the given integral formula is not correct.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫xcos⁡xdx=x22sin⁡x+C\int x \cos x d x = \frac { x ^ { 2 } } { 2 } \sin x + C∫xcosxdx=2x2​sinx+C

Use Differentiation to Determine Whether the Integral Formula Is Correct $\int x \cos x d x = \frac { x ^ { 2 } } { 2 } \sin x + C$