Solve ∫ (from 0 to 3) of sqrt{|t| wrt x

$$\int _ { 0 } ^ { 3 } \sqrt { | t | } d x$$

Evaluate

$$3\sqrt{|t|}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \sqrt{|t|}\mathrm{d}x$$

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

$$\sqrt{|t|}x$$

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.

$$\left(|t|\right)^{\frac{1}{2}}\times 3-\left(|t|\right)^{\frac{1}{2}}\times 0$$

Simplify.

$$3\sqrt{|t|}$$

Differentiate w.r.t. t

$$\frac{3sign(t)}{2\sqrt{|t|}}$$