What is area e^x,e^{5x},[0,1] ?

The answer to area e^x,e^{5x},[0,1] is -e+1+(e^5-1)/5

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area e^x,e^{5x},[0,1]

area

e^{x}, e^{5 x}, [0, 1]

- e + 1 + \frac{e ^{5} - 1}{5}

Decimal Notation

27.76434 \dots

Solution steps

Apply the area formula:

\int_{0}^{1} e^{x} - e^{5 x} d x

Solve

\int_{0}^{1} e^{x} - e^{5 x} d x : - e + 1 + \frac{e ^{5} - 1}{5}

The area is:

= - e + 1 + \frac{e ^{5} - 1}{5}

\int \frac{2}{x ( x ^{2} + 1 ) ^{2}} d x

\int \frac{1}{x ^{2} - 14 x + 58} d x

\int_{0}^{1} x x d x

\int - e^{- x} (2 x - 2) d x

y^{^{'}} - y = 2 e^{x}

What is area e^x,e^{5x},[0,1] ?
The answer to area e^x,e^{5x},[0,1] is -e+1+(e^5-1)/5