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

The integral from 0 to pi/3 of 2+sin(3x) is (2pi)/3+2/3

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

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

\frac{2 π}{3} + \frac{2}{3}

Decimal

2.76106 \dots

Solution steps

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

\int_{0}^{\frac{π}{3}} 2 d x = \frac{2 π}{3}

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

= \frac{2 π}{3} + \frac{2}{3}

\int e^{- i w x} d x

(x - 1) y^{^{'}} + y (x - 2) = 0

d er i v a t i v e f (x) = sin (2) x^{2}

x^{^{''}} - 5 x^{^{'}} + 6 x = e^{2 t}

d er i v a t i v e y = (x^{2} - 6 x + 10) 25 - x^{2}

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