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

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

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

\int_{0}^{π} (2 x - 1) cos (1 x) d x

- 4

Solution steps

\int_{0}^{π} (2 x - 1) cos (1 \cdot x) d x

Expand

(2 x - 1) cos (1 \cdot x) : 2 x cos (x) - cos (x)

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

\int_{0}^{π} 2 x cos (x) d x = - 4

\int_{0}^{π} cos (x) d x = 0

= - 4 - 0

Simplify

= - 4

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

\int_{0}^{4} (2 + 6 x) d x

\int_{- 5}^{5} (3 x - 5) d x

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

\int_{0}^{2 π} θ^{2} d θ

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