What is the integral from 0 to pi/9 of 7-7cos(3x) ?

The integral from 0 to pi/9 of 7-7cos(3x) is (7pi)/9-7/(2sqrt(3))

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integral from 0 to pi/9 of 7-7cos(3x)

\int_{0}^{\frac{π}{9}} 7 - 7 cos (3 x) d x

\frac{7 π}{9} - \frac{7}{2 3}

Decimal

0.42273 \dots

Solution steps

\int_{0}^{\frac{π}{9}} 7 - 7 cos (3 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{9}} 7 d x - \int_{0}^{\frac{π}{9}} 7 cos (3 x) d x

\int_{0}^{\frac{π}{9}} 7 d x = \frac{7 π}{9}

\int_{0}^{\frac{π}{9}} 7 cos (3 x) d x = \frac{7}{2 3}

= \frac{7 π}{9} - \frac{7}{2 3}

x \to 1 lim (- \frac{x}{x ^{2} - x})

d er i v a t i v e f (x) = (csc (3 x - 1))^{\frac{2}{3}}

\int x^{2} + 2 x d x

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{7}})

x \to 3 lim (\frac{x + 4}{x + 7})

What is the integral from 0 to pi/9 of 7-7cos(3x) ?
The integral from 0 to pi/9 of 7-7cos(3x) is (7pi)/9-7/(2sqrt(3))