Solve ∫ (from 1 to 2 frac { 5) of {3}}y wrt y

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

Evaluate

$$\frac{56}{9}\approx 6.222222222$$

Solution Steps

Evaluate the indefinite integral first.

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

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}.

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

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.

$$\frac{1}{2}\times \left(\frac{1}{3}\left(2\times 3+5\right)\right)^{2}-\frac{1^{2}}{2}$$

Simplify.

$$\frac{56}{9}$$