First slide

Integration

Question

The integral $\int_{1}^{5} x^{2} d x$ is equal to

Moderate

A

$\frac{125}{3}$
B

$\frac{124}{3}$
C

$\frac{1}{3}$
D

45

Solution

$\int_{1}^{5} x^{2} d x = {[\frac{x^{3}}{3}]}_{1}^{5} = [\frac{5^{3}}{3} - \frac{1^{3}}{3}] = \frac{125}{3} - \frac{1}{3} = \frac{124}{3}$
The correct option is 2.

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