Question

∫x² cos x dx is …

(a) x² sin x + 2x cos x – 2 sin x + c 

(b) x² sin x – 2x cos x – 2 sin x + c 

(c) -x² sin x + 2x cos x + 2 sin x + c 

(d) -x² sin x – 2x cos x + 2 sin x + c

Answer 1

(a) x² sin x + 2x cos x – 2 sin x + c 

∫x² cos x dx

By Bernoullis formula dv = cos x dx 

u = x² v = sin x 

u’ = 2x v₁ = -cos x 

u” = 2 v₂ = -sin x 

= uv – u’v₁ + u”v₂ 

= x² sin x + 2x cos x – 2 sin x + c