## University Calculus: Early Transcendentals (3rd Edition)

Differentiate each option to check the original integral. a) We have $\dfrac{d}{dx}[\dfrac{x^2}{2} \sin x+C]=x \sin x+\dfrac{x^2}{2}\ne x \sin x$ b) We have $\dfrac{d}{dx}[- x \cos x+C]=-\cos x+x \sin x \ne x \sin x$ b) We have $\dfrac{d}{dx}[- x \cos x+\sin x+C]=-\cos x+x \sin x+\cos x = x \sin x$ Hence, a) False b) False c) True