Solve ∫ (from 1 to 2) of -{(e)^x wrt x

$$\int_{ 1 }^{ 2 } - {(e)^{ x }} d x$$

Evaluate

$$e\left(1-e\right)\approx -4.67077427$$

Solution Steps

Evaluate the indefinite integral first.

$$\int -e^{x}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$-\int e^{x}\mathrm{d}x$$

Use \int e^{x}\mathrm{d}x=e^{x} from the table of common integrals to obtain the result.

$$-e^{x}$$

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.

$$-e^{2}+e^{1}$$

Simplify.

$$e\left(-e+1\right)$$