Solve ∫ (from 0 to 2) of int_0^xy wrt ydx

$$\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { x } y d y d x$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \int _{0}^{x}y\mathrm{d}y\mathrm{d}x$$

Simplify.

$$\frac{x^{3}}{6}$$

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.

$$\frac{2^{3}}{6}-\frac{0^{3}}{6}$$

Simplify.

$$\frac{4}{3}$$