What is the integral from 10 to 12 of sin(5x) ?

The integral from 10 to 12 of sin(5x) is 1/5 (-cos(60)+cos(50))

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integral from 10 to 12 of sin(5x)

\int_{10}^{12} sin (5 x) d x

\frac{1}{5} (- cos (60) + cos (50))

Decimal

0.38347 \dots

Solution steps

\int_{10}^{12} sin (5 x) d x

Apply u-substitution

: \int_{50}^{60} sin (u) \frac{1}{5} d u

= \int_{50}^{60} sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{50}^{60} sin (u) d u

Use the common integral:

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

= \frac{1}{5} [- cos (u)]_{50}^{60}

Compute the boundaries:

- cos (60) + cos (50)

= \frac{1}{5} (- cos (60) + cos (50))

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What is the integral from 10 to 12 of sin(5x) ?
The integral from 10 to 12 of sin(5x) is 1/5 (-cos(60)+cos(50))