What is the integral from 0 to pi of (2x-1)cos(5x) ?

The integral from 0 to pi of (2x-1)cos(5x) is -4/25

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integral from 0 to pi of (2x-1)cos(5x)

\int_{0}^{π} (2 x - 1) cos (5 x) d x

- \frac{4}{25}

Decimal Notation

- 0.16

Solution steps

\int_{0}^{π} (2 x - 1) cos (5 x) d x

Expand

(2 x - 1) cos (5 x) : 2 x cos (5 x) - cos (5 x)

= \int_{0}^{π} 2 x cos (5 x) - cos (5 x) 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} 2 x cos (5 x) d x - \int_{0}^{π} cos (5 x) d x

\int_{0}^{π} 2 x cos (5 x) d x = - \frac{4}{25}

\int_{0}^{π} cos (5 x) d x = 0

= - \frac{4}{25} - 0

Simplify

= - \frac{4}{25}

\int_{2}^{3} \frac{1}{2 x ^{2} + 3 x - 2} d x

\int_{1}^{e} 1 + \frac{1}{x ^{2}} d x

\int_{0}^{2} (3 x^{2}) d x

\int_{1}^{2} x^{3} - 3 x^{2} + 2 x d x

\int_{0}^{1} x^{2} 1 + 4 x^{2} d x

What is the integral from 0 to pi of (2x-1)cos(5x) ?
The integral from 0 to pi of (2x-1)cos(5x) is -4/25