Match the function with its antiderivative (a)-(d). f(x) = x sin x?

Question

(a) F (x) = cos(1-x)

(b) F (x) = -cos x

(c) F (x) = -1/2 cos(x^2)

(d) F (x) = sin x - x cos x

Answer 1

The answer will be whichever of the choices of F(x) that has derivative = x sin x.

Answer d.

F(x) = sin(x) - x cos(x)

F'(x) = cos(x) - [ - xsin(x) + cos(x) ] = xsin(x)