Solve ∫ (from 1 to 2) of 5/3y wrt y

$$\int _ { 1 } ^ { 2 } \frac { 5 } { 3 } y d y$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{5y}{3}\mathrm{d}y$$

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

$$\frac{5\int y\mathrm{d}y}{3}$$

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}.

$$\frac{5y^{2}}{6}$$

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.

$$\frac{5}{6}\times 2^{2}-\frac{5}{6}\times 1^{2}$$

Simplify.

$$\frac{5}{2}$$