Question

∫2^(x)2 ∙ x³ dx for x ∈ [log(1/3), log3] is equal to...... 

(a) 0 

(b) log3 

(c) – log3 

(d) log2

Answer 1

The correct option (a) 0  

Explanation:

I = ^log3∫_log(1/3) 2^(x)2 ∙ x³ dx 

Let f(x) = 2(x)² x³ 

f(– x) = 2(x)² (– x)³ = – f(x) 

∴ f(x) is odd function 

∴ I = ^log3∫_–log3 2(x)² ∙ x³ dx = 0.