Solve ∫ (from 1 to 3) of 3x^2 wrt y

$$\int _ { 1 } ^ { 3 } 3 x ^ { 2 } d y$$

Evaluate

$$6x^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3x^{2}\mathrm{d}y$$

Find the integral of 3x^{2} using the table of common integrals rule \int a\mathrm{d}y=ay.

$$3x^{2}y$$

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.

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

Simplify.

$$6x^{2}$$

Differentiate w.r.t. x

$$12x$$