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

The integral from-pi/2 to pi/2 of 3cos(x) is 6

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

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

6

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

2

= 3 \cdot 2

Simplify

= 6

\int_{0}^{\infty} e^{- a t} d t

\int_{- 1}^{2} x - x^{2} d x

\int_{0}^{y} x e^{- x} d x

\int_{- 1}^{2} x^{2} - 3 x - 1 d x

\int_{0}^{1} y (y + \frac{1}{2}) d y

What is the integral from-pi/2 to pi/2 of 3cos(x) ?
The integral from-pi/2 to pi/2 of 3cos(x) is 6