Question

∫(x – 1)e^–x dx = _______ + c 

(a) xe^x 

(b) – xe^–x 

(c) – xe^x 

(d) xe^–x

Answer 1

The correct option (b) – xe^–x

Explanation:

I = ∫(x – 1)e^–xdx 

I = ∫x ∙ e^–xdx – ∫e^–xdx 

∴ I = x∫e^–xdx – ∫∫e^–xdx(1) – e^–x(– 1) + c 

= xe^–x(– 1) + ∫e^–x + e^–x + c 

= – xe^–x + e^–x(– 1) + e^–x + c 

I = – xe^–x + c