$$\displaystyle\int_{ 4 }^{ 6 } { x }^{ 2 } . d x$$
Evaluate
$\frac{152}{3}\approx 50.666666667$
Solution Steps
Evaluate the indefinite integral first.
$$\int x^{2}\mathrm{d}x$$
Since $\int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1}$ for $k\neq -1$, replace $\int x^{2}\mathrm{d}x$ with $\frac{x^{3}}{3}$.
$$\frac{x^{3}}{3}$$
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.
