Solve ∫ (from 0 to frac { 2 pi) of {2}}3sqrt{5}costdt

$$\int _ { 0 } ^ { \frac { 2 \pi } { 2 } } 3 \sqrt { 5 } \cos t d t$$

Evaluate

$$0$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3\sqrt{5}\cos(t)\mathrm{d}t$$

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

$$3\sqrt{5}\int \cos(t)\mathrm{d}t$$

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

$$3\sqrt{5}\sin(t)$$

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.

$$3\times 5^{\frac{1}{2}}\sin(\frac{1}{2}\times 2\pi )-3\times 5^{\frac{1}{2}}\sin(0)$$

Simplify.

$$0$$