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

The integral from-pi/2 to pi/2 of 4cos(t) is 8

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integral from-pi/2 to pi/2 of 4cos(t)

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos (t) d t

8

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos (t) d t

Take the constant out:

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

= 4 \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (t) d t

Use the common integral:

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

= 4 [sin (t)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= 4 \cdot 2

Simplify

= 8

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What is the integral from-pi/2 to pi/2 of 4cos(t) ?
The integral from-pi/2 to pi/2 of 4cos(t) is 8