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Home / Aptitude Tests / Further Mathematics / Evaluate\({1_0^∫...

Evaluate ${1_0^∫} x^2(x^3+2)^3$ ...

Evaluate ${1_0^∫} x^2(x^3+2)^3$

A.

$\frac{56}{12}$

B.

$\frac{65}{12}$

C.

12

D.

65

View answer & explanation

Correct answer is B

${1_0^∫} x^2(x^3+2)^3$ dx

let $u = x^3 + 2, du = 3x^2dx$

when x = 1, u = 3

when x = 0, u = 2

dx = $\frac{du}{3x^2}$

${3_2^∫}$ $\frac{x^2[u]^3}{3x^2}$

${3_2^∫}$ $\frac{u^3}{3}$ du

= $\frac{u^4}{3*4}$ $_2$ 3

$\frac{1}{12} [u^4]$ $_2$ 3

$\frac{1}{12} [3^4 - 2^4]$

$\frac{1}{12}[81 - 16]$

$\frac{65}{12}$

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