Solve ∫ (from 5 to 9) of x^2x wrt x

$$\int_{ 5 }^{ 9 } { x }^{ 2 } x d x$$

Evaluate

$$1484$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\int _{5}^{9}x^{3}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int x^{3}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.

$$\frac{x^{4}}{4}$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\frac{9^{4}}{4}-\frac{5^{4}}{4}$$

Simplify.

$$1484$$