What is area e^x,(e^{2x})/2 ,0,1 ?

The answer to area e^x,(e^{2x})/2 ,0,1 is -e+(e^2-3)/4+2

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area e^x,(e^{2x})/2 ,0,1

area

e^{x}, \frac{e ^{2 x}}{2}, 0, 1

- e + \frac{e ^{2} - 3}{4} + 2

Decimal

0.37898 \dots

Solution steps

Apply the area formula:

\int_{0}^{1} e^{x} - \frac{e ^{2 x}}{2} d x

Solve

\int_{0}^{1} e^{x} - \frac{e ^{2 x}}{2} d x : - e + \frac{e ^{2} - 3}{4} + 2

The area is:

= - e + \frac{e ^{2} - 3}{4} + 2

\frac{d}{d x} (- \frac{1}{4 ( x ) ^{\frac{3}{2}}})

\frac{4 x}{( x ^{2} + 1 ) ^{2}}

y = \frac{5 x ^{2} + 8 x + 4}{x}

y = sin (3 x + 4 y)

x \to 2 lim (x^{2} + 5)

What is area e^x,(e^{2x})/2 ,0,1 ?
The answer to area e^x,(e^{2x})/2 ,0,1 is -e+(e^2-3)/4+2