What is the integral from pi/2 to (3pi)/2 of 2cos(x) ?

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

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integral from pi/2 to (3pi)/2 of 2cos(x)

\int_{\frac{π}{2}}^{\frac{3 π}{2}} 2 cos (x) d x

- 4

Solution steps

\int_{\frac{π}{2}}^{\frac{3 π}{2}} 2 cos (x) d x

Take the constant out:

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

= 2 \cdot \int_{\frac{π}{2}}^{\frac{3 π}{2}} cos (x) d x

Use the common integral:

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

= 2 [sin (x)]_{\frac{π}{2}}^{\frac{3 π}{2}}

Compute the boundaries:

- 2

= 2 (- 2)

Simplify

= - 4

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