A. −Cos x + 2xSin x + C B. −Cos x + 2 C. x2Cos x + 2xSin x + 2Cos x+ C D. −x2Cos x + 2xSinx + 2Cos x + C
Correct Answer: D
Explanation
Let u= x2 du = 2xdx Let v = sinx ∫dv = ∫ sin x i.e. v = cos x ∫ udv = uv − ∫ vdu ∫ x2 Sin xdx = − x2 Cos x − ∫ (− Cos x)2 x dx x2 Cos x + 2 ∫ x cos x1 dx = − x2 Cos x + 2 ∫ x Cos x2 dx 2 ∫ u Cos xdx Let u = x du = dx dv = Cos x ∫dv = ∫ Cos x ∫ x2 Sin x1 dx = − x2 Cos x + 2Sin x − 2Cos x + C ∫ x2 Sin xdx = − x2 Cos x + 2xSin + 2Cos x + C
