What is the integral from 0 to 3 of cos((nxpi)/3) ?

The integral from 0 to 3 of cos((nxpi)/3) is 0

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integral from 0 to 3 of cos((nxpi)/3)

\int_{0}^{3} cos (\frac{n x π}{3}) d x

0

Solution steps

\int_{0}^{3} cos (\frac{n x π}{3}) d x

Apply Integration By Parts

: [x cos (\frac{πn x}{3}) - \int - \frac{πn}{3} x sin (\frac{πn x}{3}) d x]_{0}^{3}

= [x cos (\frac{πn x}{3}) - \int - \frac{πn}{3} x sin (\frac{πn x}{3}) d x]_{0}^{3}

\int - \frac{πn}{3} x sin (\frac{πn x}{3}) d x = x cos (\frac{πn x}{3}) - \frac{3}{πn} sin (\frac{πn x}{3})

= [x cos (\frac{πn x}{3}) - (x cos (\frac{πn x}{3}) - \frac{3}{πn} sin (\frac{πn x}{3}))]_{0}^{3}

Simplify

= [\frac{3}{πn} sin (\frac{πn x}{3})]_{0}^{3}

Compute the boundaries:

0

= 0

\frac{d}{d x} (\frac{x - 1}{x + 2})

\frac{\partial}{\partial x} (\frac{x}{4} + y)

\frac{\partial}{\partial x} (b)

\frac{d}{d x} (x l)

\frac{1}{1 - x ^{2}}

What is the integral from 0 to 3 of cos((nxpi)/3) ?
The integral from 0 to 3 of cos((nxpi)/3) is 0