Solve ∫ (from 20 to 120) of 20*y wrt y

$$\int _ { 20 } ^ { 120 } 20 \cdot y d y$$

Evaluate

$$140000$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 20y\mathrm{d}y$$

Factor out the constant using \int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y.

$$20\int y\mathrm{d}y$$

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}. Multiply 20 times \frac{y^{2}}{2}.

$$10y^{2}$$

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.

$$10\times 120^{2}-10\times 20^{2}$$

Simplify.

$$140000$$