Solve ∫ (from 1 to 10) of k^2

$$\int _ { 1 } ^ { 10 } k ^ { 2 }$$

Evaluate

$$9k^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int k^{2}\mathrm{d}x$$

Find the integral of k^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$k^{2}x$$

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.

$$k^{2}\times 10-k^{2}$$

Simplify.

$$9k^{2}$$

Differentiate w.r.t. k

$$18k$$