What is the integral of 100sin(120pix) ?

The integral of 100sin(120pix) is -5/(6pi)cos(120pix)+C

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integral of 100sin(120pix)

\int 100 sin (120 π x) d x

- \frac{5}{6 π} cos (120 π x) + C

Solution steps

\int 100 sin (120 π x) d x

Take the constant out:

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

= 100 \cdot \int sin (120 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{120 π} d u

= 100 \cdot \int sin (u) \frac{1}{120 π} d u

Take the constant out:

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

= 100 \cdot \frac{1}{120 π} \cdot \int sin (u) d u

Use the common integral:

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

= 100 \cdot \frac{1}{120 π} (- cos (u))

Substitute back

u = 120 π x

= 100 \cdot \frac{1}{120 π} (- cos (120 π x))

Simplify

100 \cdot \frac{1}{120 π} (- cos (120 π x)) : - \frac{5}{6 π} cos (120 π x)

= - \frac{5}{6 π} cos (120 π x)

Add a constant to the solution

= - \frac{5}{6 π} cos (120 π x) + C

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What is the integral of 100sin(120pix) ?
The integral of 100sin(120pix) is -5/(6pi)cos(120pix)+C