What is the integral from 0 to pi of (2x-1)cos(3x) ?

The integral from 0 to pi of (2x-1)cos(3x) is -4/9

Popular >

integral from 0 to pi of (2x-1)cos(3x)

\int_{0}^{π} (2 x - 1) cos (3 x) d x

- \frac{4}{9}

Decimal Notation

- 0.44444 \dots

Solution steps

\int_{0}^{π} (2 x - 1) cos (3 x) d x

Expand

(2 x - 1) cos (3 x) : 2 x cos (3 x) - cos (3 x)

= \int_{0}^{π} 2 x cos (3 x) - cos (3 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 (3 x) d x - \int_{0}^{π} cos (3 x) d x

\int_{0}^{π} 2 x cos (3 x) d x = - \frac{4}{9}

\int_{0}^{π} cos (3 x) d x = 0

= - \frac{4}{9} - 0

Simplify

= - \frac{4}{9}

\int_{- π}^{π} 2 sin (x) d x

\int_{0}^{8} x^{3} d x

\int_{0}^{y} e^{t^{4}} d t

\int_{0}^{\frac{π}{4}} 5 sec (x) tan (x) d x

\int_{1}^{5} 4 - (x - 3)^{2} d x

What is the integral from 0 to pi of (2x-1)cos(3x) ?
The integral from 0 to pi of (2x-1)cos(3x) is -4/9