Question

If ∫xcosec²xdx = P ∙ xcotx + Q log|sinx| + C then P + Q = ______ 

(a) 1 

(b) 2 

(c) 0 

(d) – 1

Answer 1

The correct option (c) 0   

Explanation:

Let u = x 

v = cosec²x, 

by integration by parts, 

I = ∫xcosec²xdx = x∫cosec²x – ∫∫cosec²x ∙ (1) 

= x ∙ (– cotx) + ∫cotxdx 

= – xcotx + log|sinx| + c 

Comparing with 

Px cotx + Q log|sinx| + c we get 

p = – 1 and Q = 1 

∴ p + Q = 0