What is the integral from 0 to pi/2 of cos(4θ) ?

The integral from 0 to pi/2 of cos(4θ) is 0

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integral from 0 to pi/2 of cos(4θ)

\int_{0}^{\frac{π}{2}} cos (4 θ) d θ

0

Solution steps

\int_{0}^{\frac{π}{2}} cos (4 θ) d θ

Apply u-substitution

: \int_{0}^{2 π} cos (u) \frac{1}{4} d u

= \int_{0}^{2 π} cos (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{2 π} cos (u) d u

Use the common integral:

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

= \frac{1}{4} [sin (u)]_{0}^{2 π}

Compute the boundaries:

0

= \frac{1}{4} \cdot 0

Simplify

= 0

\int_{0}^{25} π (x)^{2} d x

\int_{0}^{4} x \frac{x}{8} d x

\int_{1}^{5} (1 + \frac{1}{x} + \frac{1}{x ^{2}}) d x

\int_{0}^{1} 4 y d y

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

What is the integral from 0 to pi/2 of cos(4θ) ?
The integral from 0 to pi/2 of cos(4θ) is 0