What is the integral from (3pi)/2 to 2pi of-4sin(x) ?

The integral from (3pi)/2 to 2pi of-4sin(x) is 4

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integral from (3pi)/2 to 2pi of-4sin(x)

\int_{\frac{3 π}{2}}^{2 π} - 4 sin (x) d x

4

Solution steps

\int_{\frac{3 π}{2}}^{2 π} - 4 sin (x) d x

Take the constant out:

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

= - 4 \cdot \int_{\frac{3 π}{2}}^{2 π} sin (x) d x

Use the common integral:

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

= - 4 [- cos (x)]_{\frac{3 π}{2}}^{2 π}

Compute the boundaries:

- 1

= - 4 (- 1)

Simplify

= 4

x \to - 2 lim (ln (x + 2))

\frac{d}{d x} (\frac{x}{x - 4})

\int e^{x + l n (x)} d x

\int 6 x e^{x} d x

\frac{\partial}{\partial x} (x (150 y + 60 z + 240 t))

What is the integral from (3pi)/2 to 2pi of-4sin(x) ?
The integral from (3pi)/2 to 2pi of-4sin(x) is 4