Solve ∫ (from 3 to 4) of e^a^2+3=

$$\int _ { 3 } ^ { 4 } e ^ { a ^ { 2 } + 3 } =$$

Evaluate

$$e^{a^{2}+3}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int e^{a^{2}+3}\mathrm{d}x$$

Find the integral of e^{a^{2}+3} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$e^{a^{2}+3}x$$

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.

$$e^{a^{2}+3}\times 4-e^{a^{2}+3}\times 3$$

Simplify.

$$e^{a^{2}+3}$$

Differentiate w.r.t. a

$$2ae^{a^{2}+3}$$