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)

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

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}

d er i v a t i v e \frac{141}{7 - 2}

t an g e n t f (x) = 4 x^{2} + 2 x, at x = - 2

in v erse l a pl a ce \frac{1}{s ^{2} + 6 s + 8}

in v erse l a pl a ce \frac{s}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 4 )}

\int 8 (x + 1) d x

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)