Solve ∫ (from 0 to 4) of y-2 wrt y

$$\int _ { 0 } ^ { 4 } y - 2 d y$$

Evaluate

$$0$$

Solution Steps

Evaluate the indefinite integral first.

$$\int y-2\mathrm{d}y$$

Integrate the sum term by term.

$$\int y\mathrm{d}y+\int -2\mathrm{d}y$$

Since \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} for k\neq -1, replace \int y\mathrm{d}y with \frac{y^{2}}{2}.

$$\frac{y^{2}}{2}+\int -2\mathrm{d}y$$

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

$$\frac{y^{2}}{2}-2y$$

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.

$$\frac{4^{2}}{2}-2\times 4-\left(\frac{0^{2}}{2}-2\times 0\right)$$

Simplify.

$$0$$