What is the integral of (pi-x)cos(nx) ?

The integral of (pi-x)cos(nx) is 1/n sin(nx)(pi-x)-1/(n^2)cos(nx)+C

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integral of (pi-x)cos(nx)

\int (π - x) cos (n x) d x

\frac{1}{n} sin (n x) (π - x) - \frac{1}{n ^{2}} cos (n x) + C

Solution steps

\int (π - x) cos (n x) d x

Apply Integration By Parts

: \frac{1}{n} sin (n x) (π - x) - \int - \frac{1}{n} sin (n x) d x

= \frac{1}{n} sin (n x) (π - x) - \int - \frac{1}{n} sin (n x) d x

\int - \frac{1}{n} sin (n x) d x = \frac{1}{n ^{2}} cos (n x)

= \frac{1}{n} sin (n x) (π - x) - \frac{1}{n ^{2}} cos (n x)

Add a constant to the solution

= \frac{1}{n} sin (n x) (π - x) - \frac{1}{n ^{2}} cos (n x) + C

f (x) = x^{3} + 3 x^{2} - 2 x + 1

x \to + 7 + lim (\frac{5}{x - 7})

\frac{1}{3}

\int_{0}^{8} (x^{2} + 8) e^{- x} d x

What is the integral of (pi-x)cos(nx) ?
The integral of (pi-x)cos(nx) is 1/n sin(nx)(pi-x)-1/(n^2)cos(nx)+C