What is the integral from 0 to 3 of cos((pix)/3) ?

The integral from 0 to 3 of cos((pix)/3) is 0

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integral from 0 to 3 of cos((pix)/3)

\int_{0}^{3} cos (\frac{π x}{3}) d x

0

Solution steps

\int_{0}^{3} cos (\frac{π x}{3}) d x

Apply u-substitution

: \int_{0}^{π} cos (u) \frac{3}{π} d u

= \int_{0}^{π} cos (u) \frac{3}{π} d u

Take the constant out:

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

= \frac{3}{π} \cdot \int_{0}^{π} cos (u) d u

Use the common integral:

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

= \frac{3}{π} [sin (u)]_{0}^{π}

Compute the boundaries:

0

= \frac{3}{π} \cdot 0

Simplify

= 0

x \to 0 lim ((1 - x)^{\frac{5}{x}})

f (x) = sin^{2} (x^{2})

\int \frac{x ^{4} + x - 4}{x ^{2} + 2} d x

\frac{d}{d x} (\frac{x}{x ^{2} + 64})

\frac{d y}{d x} (x^{2}) = y^{3}

What is the integral from 0 to 3 of cos((pix)/3) ?
The integral from 0 to 3 of cos((pix)/3) is 0