What is the integral from 0 to pi of (3x+7)*cos(x) ?

The integral from 0 to pi of (3x+7)*cos(x) is -6

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integral from 0 to pi of (3x+7)*cos(x)

\int_{0}^{π} (3 x + 7) \cdot cos (x) d x

- 6

Solution steps

\int_{0}^{π} (3 x + 7) cos (x) d x

Apply Integration By Parts

: [(3 x + 7) sin (x) - \int 3 sin (x) d x]_{0}^{π}

= [(3 x + 7) sin (x) - \int 3 sin (x) d x]_{0}^{π}

\int 3 sin (x) d x = - 3 cos (x)

= [(3 x + 7) sin (x) - (- 3 cos (x))]_{0}^{π}

Simplify

= [sin (x) (3 x + 7) + 3 cos (x)]_{0}^{π}

Compute the boundaries:

- 6

= - 6

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What is the integral from 0 to pi of (3x+7)*cos(x) ?
The integral from 0 to pi of (3x+7)*cos(x) is -6