What is area x=e^{2y},y=0,x=e^4 ?

The answer to area x=e^{2y},y=0,x=e^4 is 82.39722…

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area x=e^{2y},y=0,x=e^4

area

x = e^{2 y}, y = 0, x = e^{4}

82.39722 \dots

Solution steps

Isolate

y

for

x = e^{2 y} : y = \frac{ln ( x )}{2}

Apply the area formula:

\int_{1}^{e^{4}} \frac{1}{2} ∣ ln (x) ∣ d x

Solve

\int_{1}^{e^{4}} \frac{1}{2} ∣ ln (x) ∣ d x : 82.39722 \dots

The area is:

= 82.39722 \dots

y = x^{2}, y = 5

\frac{d}{d x} (11 cos (x))

y = \frac{x ^{2} - 1}{x ^{2} + x + 1} (1)

\frac{d}{d x} (2 x + e^{x})

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

What is area x=e^{2y},y=0,x=e^4 ?
The answer to area x=e^{2y},y=0,x=e^4 is 82.39722…