What is the integral of 100sin(500x) ?

The integral of 100sin(500x) is -1/5 cos(500x)+C

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integral of 100sin(500x)

\int 100 sin (500 x) d x

- \frac{1}{5} cos (500 x) + C

Solution steps

\int 100 sin (500 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 (500 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{500} d u

= 100 \cdot \int sin (u) \frac{1}{500} d u

Take the constant out:

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

= 100 \cdot \frac{1}{500} \cdot \int sin (u) d u

Use the common integral:

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

= 100 \cdot \frac{1}{500} (- cos (u))

Substitute back

u = 500 x

= 100 \cdot \frac{1}{500} (- cos (500 x))

Simplify

100 \cdot \frac{1}{500} (- cos (500 x)) : - \frac{1}{5} cos (500 x)

= - \frac{1}{5} cos (500 x)

Add a constant to the solution

= - \frac{1}{5} cos (500 x) + C

\frac{1}{8 x} \frac{d y}{d x} = y 4 x^{2} - 1

\int 5 - 0.04 x + 3 x^{2} d x

\frac{d}{d x} (\frac{2 x}{x ^{2} - 36})

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 9

x \to - π lim (csc (x))

What is the integral of 100sin(500x) ?
The integral of 100sin(500x) is -1/5 cos(500x)+C