Question

∫cosxd(sinx) = _______ + c 

(a) [(sin2x)/2] – x 

(b) (1/2)[{(sin2x)/2} – x] 

(c) (1/2)[{(sin2x)/2} + x] 

(d) [{(sin2x)/2} + x]

Answer 1

The correct option (c) (1/2)[{(sin2x)/2} + x]  

Explanation:

I = ∫cosx ∙ d(sinx) = ∫cosx cosx dx = ∫cos²xdx = ∫[(1 + cos2x)/2]dx 

∴ I = (1/2)[x + {(sin2x)/2}] + c 

= (1/2) [{(sin2x)/2} + x] + c