What is area y=e^x,y=e^{-3x},x=-2,x=1 ?

The answer to area y=e^x,y=e^{-3x},x=-2,x=1 is e+(e^9-2e^3+3e+1)/(3e^3)-2

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area y=e^x,y=e^{-3x},x=-2,x=1

area

y = e^{x}, y = e^{- 3 x}, x = - 2, x = 1

e + \frac{e ^{9} - 2 e ^{3} + 3 e + 1}{3 e ^{3}} - 2

Decimal Notation

134.67981 \dots

Solution steps

Apply the area formula:

\int_{- 2}^{1} e^{x} - e^{- 3 x} d x

Solve

\int_{- 2}^{1} e^{x} - e^{- 3 x} d x : e + \frac{e ^{9} - 2 e ^{3} + 3 e + 1}{3 e ^{3}} - 2

The area is:

= e + \frac{e ^{9} - 2 e ^{3} + 3 e + 1}{3 e ^{3}} - 2

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

\int \frac{3}{2 + 3 x} d x

x \to 4 + lim (\frac{x - 2}{x - 4})

\int 2 x tan (x^{2}) d x

x \to - 3 lim (\frac{4 x}{x - 3})

What is area y=e^x,y=e^{-3x},x=-2,x=1 ?
The answer to area y=e^x,y=e^{-3x},x=-2,x=1 is e+(e^9-2e^3+3e+1)/(3e^3)-2