What is area y=e^x,y=e^{-2x},x=ln(6) ?

The answer to area y=e^x,y=e^{-2x},x=ln(6) is 325/72

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area y=e^x,y=e^{-2x},x=ln(6)

area

y = e^{x}, y = e^{- 2 x}, x = ln (6)

\frac{325}{72}

Decimal

4.51388 \dots

Solution steps

Apply the area formula:

\int_{0}^{l n (6)} e^{x} - e^{- 2 x} d x

Solve

\int_{0}^{l n (6)} e^{x} - e^{- 2 x} d x : \frac{325}{72}

The area is:

= \frac{325}{72}

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

\frac{480 x}{( x ^{2} + 5 ) ^{3}}

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

f (x) = (x^{2} - 8)^{2}

\frac{d}{d x} (x^{2} I n x)

What is area y=e^x,y=e^{-2x},x=ln(6) ?
The answer to area y=e^x,y=e^{-2x},x=ln(6) is 325/72