Solve ∫ _{-pi/2}^frac{pi{2}}(Hcosx) wrt x

$$\int _ { - \frac { \pi } { 2 } } ^ { \frac { \pi } { 2 } } ( H \cos x ) d x$$

Evaluate

$$2H$$

Solution Steps

Evaluate the indefinite integral first.

$$\int H\cos(x)\mathrm{d}x$$

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

$$H\int \cos(x)\mathrm{d}x$$

Use \int \cos(H)\mathrm{d}H=\sin(H) from the table of common integrals to obtain the result.

$$H\sin(x)$$

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.

$$H\sin(\frac{1}{2}\pi )-H\sin(-\frac{1}{2}\pi )$$

Simplify.

$$2H$$

Differentiate w.r.t. H

$$2$$