What is the integral from-pi to 0 of sin(3x) ?

The integral from-pi to 0 of sin(3x) is -2/3

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integral from-pi to 0 of sin(3x)

\int_{- π}^{0} sin (3 x) d x

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

\int_{- π}^{0} sin (3 x) d x

Apply u-substitution

: \int_{- 3 π}^{0} sin (u) \frac{1}{3} d u

= \int_{- 3 π}^{0} sin (u) \frac{1}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- 3 π}^{0} sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{3} [- cos (u)]_{- 3 π}^{0}

Compute the boundaries:

- 2

= \frac{1}{3} (- 2)

Simplify

= - \frac{2}{3}

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\int_{1}^{6} \frac{4 x ^{2} - 3}{x ^{3}} d x

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What is the integral from-pi to 0 of sin(3x) ?
The integral from-pi to 0 of sin(3x) is -2/3