Solve ∫ (from 0 to 3) of x^2 wrt y

$$\int _ { 0 } ^ { 3 } x ^ { 2 } d y$$

Evaluate

$$3x^{2}$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$x^{2}y$$

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.

$$x^{2}\times 3-x^{2}\times 0$$

Simplify.

$$3x^{2}$$

Differentiate w.r.t. x

$$6x$$