What is the integral from 0 to pi/(21) of cos(7x) ?

The integral from 0 to pi/(21) of cos(7x) is (sqrt(3))/(14)

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integral from 0 to pi/(21) of cos(7x)

\int_{0}^{\frac{π}{21}} cos (7 x) d x

\frac{3}{14}

Decimal

0.12371 \dots

Solution steps

\int_{0}^{\frac{π}{21}} cos (7 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{3}} cos (u) \frac{1}{7} d u

= \int_{0}^{\frac{π}{3}} cos (u) \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{0}^{\frac{π}{3}} cos (u) d u

Use the common integral:

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

= \frac{1}{7} [sin (u)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{3}{2}

= \frac{1}{7} \cdot \frac{3}{2}

Simplify

= \frac{3}{14}

\frac{141}{7 - 2}

f (x) = - 3 x - 2 3 x^{2}

\frac{\partial}{\partial x} (3 x^{2} - 2 x y - y)

\int x^{2} d x

\frac{x ^{6}}{6}

What is the integral from 0 to pi/(21) of cos(7x) ?
The integral from 0 to pi/(21) of cos(7x) is (sqrt(3))/(14)