Solve ∫ _{-sqrt{y}}^sqrt{y}1 wrt x

$$\int _ { - \sqrt { y } } ^ { \sqrt { y } } 1 d x$$

Evaluate

$$2\sqrt{y}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 1\mathrm{d}x$$

Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$x$$

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.

$$y^{\frac{1}{2}}+y^{\frac{1}{2}}$$

Simplify.

$$2\sqrt{y}$$

Differentiate w.r.t. y

$$\frac{1}{\sqrt{y}}$$