Solve ∫ (from 1 to sqrt { 3) of }2e

$$\int _ { 1 } ^ { \sqrt { 3 } } 2 e$$

Evaluate

$$2e\left(\sqrt{3}-1\right)\approx 3.979840815$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2e\mathrm{d}x$$

Find the integral of 2e using the table of common integrals rule \int a\mathrm{d}x=ax.

$$2ex$$

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.

$$2e\times 3^{\frac{1}{2}}-2e$$

Simplify.

$$2e\left(\sqrt{3}-1\right)$$