Solve ∫ (from 0 to 2) of 9/2y wrt y

$$\int _ { 0 } ^ { 2 } \frac { 9 } { 2 } y d y$$

Evaluate

$$9$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{9y}{2}\mathrm{d}y$$

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

$$\frac{9\int y\mathrm{d}y}{2}$$

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}.

$$\frac{9y^{2}}{4}$$

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.

$$\frac{9}{4}\times 2^{2}-\frac{9}{4}\times 0^{2}$$

Simplify.

$$9$$