Solve ∫ (from 0 to 1 / 2) of (y/2-y/2)^2 wrt y

$$\int _ { 0 } ^ { 1 / 2 } ( \frac { y } { 2 } - \frac { y } { 2 } ) ^ { 2 } d y$$

Evaluate

$$0$$

Solution Steps

Combine \frac{y}{2} and -\frac{y}{2} to get 0.

$$\int _{0}^{\frac{1}{2}}0^{2}\mathrm{d}y$$

Calculate 0 to the power of 2 and get 0.

$$\int _{0}^{\frac{1}{2}}0\mathrm{d}y$$

Evaluate the indefinite integral first.

$$\int 0\mathrm{d}y$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}y=ay.

$$0$$

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.

$$0+0$$

Simplify.

$$0$$