What is the integral from 0 to (3pi)/2 of 5sin(x) ?

The integral from 0 to (3pi)/2 of 5sin(x) is 5

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integral from 0 to (3pi)/2 of 5sin(x)

\int_{0}^{\frac{3 π}{2}} 5 sin (x) d x

5

Solution steps

\int_{0}^{\frac{3 π}{2}} 5 sin (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{\frac{3 π}{2}} sin (x) d x

Use the common integral:

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

= 5 [- cos (x)]_{0}^{\frac{3 π}{2}}

Compute the boundaries:

1

= 5 \cdot 1

Simplify

= 5

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\int_{1}^{e} \frac{4 ln ( x )}{x} d x

What is the integral from 0 to (3pi)/2 of 5sin(x) ?
The integral from 0 to (3pi)/2 of 5sin(x) is 5