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Home / Aptitude Tests / Mathematics / Evaluate \(\int^{2} ...

Evaluate $\int^{2} _{3}(x^2 - 2x)dx$
...

Evaluate $\int^{2} _{3}(x^2 - 2x)dx$

A.

4

B.

2

C.

4/3

D.

1/3

View answer & explanation

Correct answer is C

$\int^{2} _{3}(x^2 - 2x)dx\\=\left[\frac{x^3}{3}-\frac{2x^2}{2}\right ]^{2}_{3}\\\left[\frac{x^3}{3}-x^2 + C\right ]^{2}_{3}\\\left[\frac{3^3}{3}-3^2 + C \right ]-\left[\frac{2^3}{3}-2^2 + C \right ]\\9-9-\left[\frac{8}{3}-4 \right ]\\=\frac{-8}{3}+4\\=\frac{4}{3}$

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