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

The integral from-pi/4 to pi/4 of cos(2x) is 1

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

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

1

Solution steps

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

Apply u-substitution

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

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 (u) d u

Use the common integral:

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

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

Compute the boundaries:

2

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

Simplify

= 1

What is the integral from-pi/4 to pi/4 of cos(2x) ?
The integral from-pi/4 to pi/4 of cos(2x) is 1