Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 239: 63

a) False b) False c) True

Need to differentiate each option to check whether the original integral is true or not. a) $\dfrac{d}{dx}[\dfrac{x^2}{2} \sin x+C]=x \sin x+\dfrac{x^2}{2}\ne x \sin x$; False b) $\dfrac{d}{dx}[- x \cos x+C]=-\cos x+x \sin x \ne x \sin x$; False c) $\dfrac{d}{dx}[- x \cos x+\sin x+C]=-\cos x+x \sin x+\cos x = x \sin x$ ; True