What is the integral of sin(2pi*1000x) ?

The integral of sin(2pi*1000x) is -1/(2000pi)cos(2000pix)+C

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integral of sin(2pi*1000x)

\int sin (2 π \cdot 1000 x) d x

- \frac{1}{2000 π} cos (2000 π x) + C

Solution steps

\int sin (2 π 1000 x) d x

Apply Integration By Parts

: x sin (2000 π x) - \int 2000 π x cos (2000 π x) d x

= x sin (2000 π x) - \int 2000 π x cos (2000 π x) d x

\int 2000 π x cos (2000 π x) d x = x sin (2000 π x) + \frac{1}{2000 π} cos (2000 π x)

= x sin (2000 π x) - (x sin (2000 π x) + \frac{1}{2000 π} cos (2000 π x))

Simplify

= - \frac{1}{2000 π} cos (2000 π x)

Add a constant to the solution

= - \frac{1}{2000 π} cos (2000 π x) + C

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What is the integral of sin(2pi*1000x) ?
The integral of sin(2pi*1000x) is -1/(2000pi)cos(2000pix)+C