What is area y=e^x,y=e^{3x},x=0,x=ln(4) ?

The answer to area y=e^x,y=e^{3x},x=0,x=ln(4) is 18

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area y=e^x,y=e^{3x},x=0,x=ln(4)

area

y = e^{x}, y = e^{3 x}, x = 0, x = ln (4)

18

Solution steps

Apply the area formula:

\int_{0}^{l n (4)} e^{x} - e^{3 x} d x

Solve

\int_{0}^{l n (4)} e^{x} - e^{3 x} d x : 18

The area is:

= 18

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\int \frac{2}{x} - \frac{3}{x ^{4}} d x

\frac{d}{d x} y + 3 y = 0

(5, - 3), (- 1, - 1)

x \to 0 lim (\frac{x - 45}{x - 5})

What is area y=e^x,y=e^{3x},x=0,x=ln(4) ?
The answer to area y=e^x,y=e^{3x},x=0,x=ln(4) is 18