Solve ∫ (from 0 to frac{ pi) of { 2}}{(e)^x}*cos(x) wrt x

$$\int_{ 0 }^{ \frac{ \pi }{ 2 } } {(e)^{ x }} \times \cos ( x ) d x$$

Evaluate

$$e^{\frac{\pi }{2}}-1\approx 3.810477381$$

Solution Steps

Evaluate the indefinite integral first.

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

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.

$$e^{\frac{1}{2}\pi }-e^{0}$$

Simplify.

$$e^{\frac{\pi }{2}}-1$$