What is area 2cos(2x),2-2cos(2x),[0, pi/2 ] ?

The answer to area 2cos(2x),2-2cos(2x),[0, pi/2 ] is -(2pi)/3+pi+2sqrt(3)

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area 2cos(2x),2-2cos(2x),[0, pi/2 ]

area

2 cos (2 x), 2 - 2 cos (2 x), [0, \frac{π}{2}]

- \frac{2 π}{3} + π + 23

Decimal Notation

4.51129 \dots

Solution steps

Apply the area formula:

\int_{0}^{\frac{π}{2}} ∣ 2 cos (2 x) - (2 - 2 cos (2 x)) ∣ d x

Solve

\int_{0}^{\frac{π}{2}} ∣ 2 cos (2 x) - (2 - 2 cos (2 x)) ∣ d x : - \frac{2 π}{3} + π + 23

The area is:

= - \frac{2 π}{3} + π + 23

(6 x + 1)^{2}

\frac{- x ^{2} - 3}{( x ^{2} - 3 ) ^{2}}

\frac{d ^{2}}{d x ^{2}} (3 x^{- 3} + 5 x^{2})

\int \frac{x}{( 2 x + 1 ) ^{3}} d x

What is area 2cos(2x),2-2cos(2x),[0, pi/2 ] ?
The answer to area 2cos(2x),2-2cos(2x),[0, pi/2 ] is -(2pi)/3+pi+2sqrt(3)