Solve ∫ (from 0 to 4) of e^2sqrt{2pi+1 wrt x

$$\int _ { 0 } ^ { 4 } e ^ { 2 \sqrt { 2 \pi + 1 } } d x$$

Evaluate

$$4e^{2\sqrt{2\pi +1}}\approx 883.392677994$$

Solution Steps

Evaluate the indefinite integral first.

$$\int e^{2\sqrt{2\pi +1}}\mathrm{d}x$$

Find the integral of e^{2\sqrt{2\pi +1}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$e^{2\sqrt{2\pi +1}}x$$

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.

$$e^{2\left(2\pi +1\right)^{\frac{1}{2}}}\times 4-e^{2\left(2\pi +1\right)^{\frac{1}{2}}}\times 0$$

Simplify.

$$4e^{2\sqrt{2\pi +1}}$$