Evaluate the integral of x squared with respect to x.

A. x^33 + C — Using the power rule for integration, the integral of x to the power of n is x to the power of n plus 1 divided by n plus 1. Applying this to x squared gives x cubed divided by 3 plus the constant of integration.

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$\int x^{2} d x$

A. $\frac{x ^{3}}{3} + C$
B. $$2x + C$$
C. $x^{3} + C$
D. $\frac{x ^{2}}{2} + C$

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Correct answer: A — $\frac{x ^{3}}{3} + C$

Solution

\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C . For n = 2, we get \frac{x ^{3}}{3} + C .

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∫x2dx

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