Solve ∫ (from - pi to pi) of e^t^2

$$\int _ { - \pi } ^ { \pi } e ^ { t ^ { 2 } }$$

Evaluate

$$2\pi e^{t^{2}}$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$e^{t^{2}}x$$

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.

$$e^{t^{2}}\pi -e^{t^{2}}\left(-1\right)\pi$$

Simplify.

$$2e^{t^{2}}\pi$$

Differentiate w.r.t. t

$$4\pi te^{t^{2}}$$