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 Notation

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}

\int x^{2} 7 + x d x

\int t^{2} 7 t - 5 d t

x \to 0 + lim (ln ∣ x ∣)

4 sec^{2} (x)

\frac{x ^{2}}{7 + 4 x}

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