What is the integral from 0 to pi/2 of cos((2x)/3) ?

The integral from 0 to pi/2 of cos((2x)/3) is (3sqrt(3))/4

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integral from 0 to pi/2 of cos((2x)/3)

\int_{0}^{\frac{π}{2}} cos (\frac{2 x}{3}) d x

\frac{3 3}{4}

Decimal

1.29903 \dots

Solution steps

\int_{0}^{\frac{π}{2}} cos (\frac{2 x}{3}) d x

Apply u-substitution

: \int_{0}^{\frac{π}{3}} cos (u) \frac{3}{2} d u

= \int_{0}^{\frac{π}{3}} cos (u) \frac{3}{2} d u

Take the constant out:

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

= \frac{3}{2} \cdot \int_{0}^{\frac{π}{3}} cos (u) d u

Use the common integral:

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

= \frac{3}{2} [sin (u)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{3}{2}

= \frac{3}{2} \cdot \frac{3}{2}

Simplify

= \frac{3 3}{4}

f (x) = x^{3} - x, at x = 1

x 3 x - 4

n = 1 \sum \infty 2 (- e)^{- n}

\int \frac{x ^{5}}{x ^{2} + 7} d x

\int \frac{1}{5 + 4 x - x ^{2}} d x

What is the integral from 0 to pi/2 of cos((2x)/3) ?
The integral from 0 to pi/2 of cos((2x)/3) is (3sqrt(3))/4