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

The answer to area y=e^x,y=e^{3x},x=0,x=ln(3) is 20/3

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

area

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

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

Apply the area formula:

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

Solve

\int_{0}^{l n (3)} e^{x} - e^{3 x} d x : \frac{20}{3}

The area is:

= \frac{20}{3}

x \to 3 lim (ln (3 - x))

e^{11 x}

\int 2 e^{x} d x

\frac{1}{3}

\int \frac{3 x + 11}{x ^{2} - 2 x - 3} d x

What is area y=e^x,y=e^{3x},x=0,x=ln(3) ?
The answer to area y=e^x,y=e^{3x},x=0,x=ln(3) is 20/3