Solve ∫ (from 1 to frac { pi) of {3}}sqrt{3}cosx wrt x=

$$\int _ { 1 } ^ { \frac { \pi } { 3 } } \sqrt { 3 } \cos x d x =$$

Evaluate

$$\frac{\sqrt{3}\left(\sqrt{3}-2\sin(1)\right)}{2}\approx 0.042529501$$

Solution Steps

Evaluate the indefinite integral first.

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

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

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

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

$$\sqrt{3}\sin(x)$$

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.

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

Simplify.

$$\frac{1}{2}\left(3-2\sqrt{3}\sin(1)\right)$$