What is the integral from-pi/2 to pi/2 of 1/2 cos(x) ?

The integral from-pi/2 to pi/2 of 1/2 cos(x) is 1

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integral from-pi/2 to pi/2 of 1/2 cos(x)

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

1

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x

Use the common integral:

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

= \frac{1}{2} [sin (x)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= \frac{1}{2} \cdot 2

Simplify

= 1

\int_{- 4}^{4} x - 2 d x

\int_{0}^{4} \frac{1}{e ^{x} + 1} d x

\int_{0}^{1} \frac{y ^{2}}{2} d y

\int_{2}^{3} \frac{1}{x ^{2} - 6 x + 10} d x

\int_{1}^{4} \frac{x}{1 + x ^{2}} d x

What is the integral from-pi/2 to pi/2 of 1/2 cos(x) ?
The integral from-pi/2 to pi/2 of 1/2 cos(x) is 1