Solve ∫ (from 2 to 8) of 2y^2 wrt x

$$\int _ { 2 } ^ { 8 } 2 y ^ { 2 } d x$$

Evaluate

$$12y^{2}$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$2y^{2}x$$

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.

$$2y^{2}\times 8-2y^{2}\times 2$$

Simplify.

$$12y^{2}$$

Differentiate w.r.t. y

$$24y$$