What is the integral from-pi/2 to pi/2 of 5cos(t) ?

The integral from-pi/2 to pi/2 of 5cos(t) is 10

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integral from-pi/2 to pi/2 of 5cos(t)

\int_{- \frac{π}{2}}^{\frac{π}{2}} 5 cos (t) d t

10

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} 5 cos (t) d t

Take the constant out:

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

= 5 \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (t) d t

Use the common integral:

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

= 5 [sin (t)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= 5 \cdot 2

Simplify

= 10

What is the integral from-pi/2 to pi/2 of 5cos(t) ?
The integral from-pi/2 to pi/2 of 5cos(t) is 10