Solve ∫ (from 0 to frac { pi) of {2}}-cosx wrt x

$$\int _ { 0 } ^ { \frac { \pi } { 2 } } - \cos x d x$$

Evaluate

$$-1$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$-\sin(x)$$

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.

$$-\sin(\frac{1}{2}\pi )+\sin(0)$$

Simplify.

$$-1$$