What is the integral of 5sin(6pit) ?

The integral of 5sin(6pit) is -5/(6pi)cos(6pit)+C

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integral of 5sin(6pit)

\int 5 sin (6 π t) d t

- \frac{5}{6 π} cos (6 π t) + C

Solution steps

\int 5 sin (6 π t) d t

Take the constant out:

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

= 5 \cdot \int sin (6 π t) d t

Apply u-substitution

= 5 \cdot \int sin (u) \frac{1}{6 π} d u

Take the constant out:

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

= 5 \cdot \frac{1}{6 π} \cdot \int sin (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{6 π} (- cos (u))

Substitute back

u = 6 π t

= 5 \cdot \frac{1}{6 π} (- cos (6 π t))

Simplify

5 \cdot \frac{1}{6 π} (- cos (6 π t)) : - \frac{5}{6 π} cos (6 π t)

= - \frac{5}{6 π} cos (6 π t)

Add a constant to the solution

= - \frac{5}{6 π} cos (6 π t) + C

What is the integral of 5sin(6pit) ?
The integral of 5sin(6pit) is -5/(6pi)cos(6pit)+C