What is the integral of 10sin(1000pix) ?

The integral of 10sin(1000pix) is -1/(100pi)cos(1000pix)+C

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integral of 10sin(1000pix)

\int 10 sin (1000 π x) d x

- \frac{1}{100 π} cos (1000 π x) + C

Solution steps

\int 10 sin (1000 π x) d x

Take the constant out:

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

= 10 \cdot \int sin (1000 π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{1000 π} d u

= 10 \cdot \int sin (u) \frac{1}{1000 π} d u

Take the constant out:

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

= 10 \cdot \frac{1}{1000 π} \cdot \int sin (u) d u

Use the common integral:

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

= 10 \cdot \frac{1}{1000 π} (- cos (u))

Substitute back

u = 1000 π x

= 10 \cdot \frac{1}{1000 π} (- cos (1000 π x))

Simplify

10 \cdot \frac{1}{1000 π} (- cos (1000 π x)) : - \frac{1}{100 π} cos (1000 π x)

= - \frac{1}{100 π} cos (1000 π x)

Add a constant to the solution

= - \frac{1}{100 π} cos (1000 π x) + C

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What is the integral of 10sin(1000pix) ?
The integral of 10sin(1000pix) is -1/(100pi)cos(1000pix)+C