What is area tan(3x),2sin(3x),[-pi/9 , pi/9 ] ?

The answer to area tan(3x),2sin(3x),[-pi/9 , pi/9 ] is (-2ln(2)+2)/3

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area tan(3x),2sin(3x),[-pi/9 , pi/9 ]

area

tan (3 x), 2 sin (3 x), [- \frac{π}{9}, \frac{π}{9}]

\frac{- 2 ln ( 2 ) + 2}{3}

Decimal

0.20456 \dots

Solution steps

Apply the area formula:

\int_{- \frac{π}{9}}^{\frac{π}{9}} ∣ tan (3 x) - 2 sin (3 x) ∣ d x

Solve

\int_{- \frac{π}{9}}^{\frac{π}{9}} ∣ tan (3 x) - 2 sin (3 x) ∣ d x : \frac{- 2 ln ( 2 ) + 2}{3}

The area is:

= \frac{- 2 ln ( 2 ) + 2}{3}

What is area tan(3x),2sin(3x),[-pi/9 , pi/9 ] ?
The answer to area tan(3x),2sin(3x),[-pi/9 , pi/9 ] is (-2ln(2)+2)/3