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

The integral from 0 to pi of 3sin(x/3) is 9/2

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

\int_{0}^{π} 3 sin (\frac{x}{3}) d x

\frac{9}{2}

Decimal Notation

4.5

Solution steps

\int_{0}^{π} 3 sin (\frac{x}{3}) d x

Take the constant out:

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

= 3 \cdot \int_{0}^{π} sin (\frac{x}{3}) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= 3 \cdot 3 [- cos (u)]_{0}^{\frac{π}{3}}

Simplify

= 9 [- cos (u)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{1}{2}

= 9 \cdot \frac{1}{2}

Simplify

= \frac{9}{2}

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What is the integral from 0 to pi of 3sin(x/3) ?
The integral from 0 to pi of 3sin(x/3) is 9/2