What is the integral from 0 to pi of (1-x/pi)cos(lx) ?

The integral from 0 to pi of (1-x/pi)cos(lx) is (sin(pil))/l-(pilsin(pil)+cos(pil)-1)/(pil^2)

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integral from 0 to pi of (1-x/pi)cos(lx)

\int_{0}^{π} (1 - \frac{x}{π}) cos (l x) d x

\frac{sin ( π l )}{l} - \frac{π l sin ( π l ) + cos ( π l ) - 1}{π l ^{2}}

Solution steps

\int_{0}^{π} (1 - \frac{x}{π}) cos (l x) d x

Expand

(1 - \frac{x}{π}) cos (l x) : cos (l x) - \frac{x cos ( l x )}{π}

= \int_{0}^{π} cos (l x) - \frac{x cos ( l x )}{π} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{π} cos (l x) d x - \int_{0}^{π} \frac{x cos ( l x )}{π} d x

\int_{0}^{π} cos (l x) d x = \frac{sin ( π l )}{l}

\int_{0}^{π} \frac{x cos ( l x )}{π} d x = \frac{π l sin ( π l ) + cos ( π l ) - 1}{π l ^{2}}

= \frac{sin ( π l )}{l} - \frac{π l sin ( π l ) + cos ( π l ) - 1}{π l ^{2}}

\int_{0}^{a} \frac{1}{( a - x )} d x

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\int_{0}^{l n (11)} tanh (x) d x

\int_{0}^{1} \frac{( 2 x ^{2} - 5 )}{x} d x

\int_{0}^{1.2} e^{- x} cos (x) d x

What is the integral from 0 to pi of (1-x/pi)cos(lx) ?
The integral from 0 to pi of (1-x/pi)cos(lx) is (sin(pil))/l-(pilsin(pil)+cos(pil)-1)/(pil^2)