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 If the value of the integral 01/2x21-x23/2 dx is k6+π , then k is equal to: 

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a
32+π
b
23
c
32−π
d
23+π

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detailed solution

Correct option is B

Consider the integral I=∫012x21-x232dx Substitute x=sinθ,dx=cosθdθ and the limits are 0,π6 Hence, the given integral becomes I=∫0π6sin2θcos3θcosθdθ=∫0π6tan2θ  dθ=∫0π6sec2θ−1  dθ=tanθ−θ0π6=13−π6 Therefore, k6+π=13-π6=6-3π63+π, it implies k=23


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