What is the integral from pi to 3pi of 15cos(5x) ?

The integral from pi to 3pi of 15cos(5x) is 0

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integral from pi to 3pi of 15cos(5x)

\int_{π}^{3 π} 15 cos (5 x) d x

0

Solution steps

\int_{π}^{3 π} 15 cos (5 x) d x

Take the constant out:

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

= 15 \cdot \int_{π}^{3 π} cos (5 x) d x

Apply u-substitution

: \int_{5 π}^{15 π} cos (u) \frac{1}{5} d u

= 15 \cdot \int_{5 π}^{15 π} cos (u) \frac{1}{5} d u

Take the constant out:

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

= 15 \cdot \frac{1}{5} \cdot \int_{5 π}^{15 π} cos (u) d u

Use the common integral:

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

= 15 \cdot \frac{1}{5} [sin (u)]_{5 π}^{15 π}

Simplify

15 \cdot \frac{1}{5} [sin (u)]_{5 π}^{15 π} : 3 [sin (u)]_{5 π}^{15 π}

= 3 [sin (u)]_{5 π}^{15 π}

Compute the boundaries:

0

= 3 \cdot 0

Simplify

= 0

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What is the integral from pi to 3pi of 15cos(5x) ?
The integral from pi to 3pi of 15cos(5x) is 0