What is area y=sin(2x),y=cos(2x),x=0,x= pi/4 ?

The answer to area y=sin(2x),y=cos(2x),x=0,x= pi/4 is sqrt(2)-1

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area y=sin(2x),y=cos(2x),x=0,x= pi/4

area

y = sin (2 x), y = cos (2 x), x = 0, x = \frac{π}{4}

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

Apply the area formula:

\int_{0}^{\frac{π}{4}} ∣ sin (2 x) - cos (2 x) ∣ d x

Solve

\int_{0}^{\frac{π}{4}} ∣ sin (2 x) - cos (2 x) ∣ d x : 2 - 1

The area is:

= 2 - 1

2 x^{2} - 10 x + 9

\frac{4 x ^{2} - 3}{x - 1}

\frac{2}{3 x + 5}

\int \frac{cot ( x )}{ln ( sin ( x ) )} d x

x \to 3 - lim (\frac{x ^{3}}{x ^{2} - 9})

What is area y=sin(2x),y=cos(2x),x=0,x= pi/4 ?
The answer to area y=sin(2x),y=cos(2x),x=0,x= pi/4 is sqrt(2)-1