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Popular >

area e^{-x},(x+1)^2,x=1

Solution

area

e^{- x}, (x + 1)^{2}, x = 1

Solution

- e^{- 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 1} + \frac{1}{e} + \frac{- 8 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{3} + 12 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{2} - 6 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) + 2}{3} - 4 W_{0} (\frac{e ^{\frac{1}{2}}}{2})^{2} + 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 2

+1

Decimal Notation

1.70121 \dots

Solution steps

Apply the area formula:

\int_{2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) - 1}^{1} e^{- x} - (x + 1)^{2} d x

Solve

\int_{2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) - 1}^{1} e^{- x} - (x + 1)^{2} d x : - e^{- 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 1} + \frac{1}{e} + \frac{- 8 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{3} + 12 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{2} - 6 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) + 2}{3} - 4 W_{0} (\frac{e ^{\frac{1}{2}}}{2})^{2} + 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 2

The area is:

= - e^{- 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 1} + \frac{1}{e} + \frac{- 8 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{3} + 12 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) ^{2} - 6 W _{0} ( \frac{e ^{\frac{1}{2}}}{2} ) + 2}{3} - 4 W_{0} (\frac{e ^{\frac{1}{2}}}{2})^{2} + 2 W_{0} (\frac{e ^{\frac{1}{2}}}{2}) + 2

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Frequently Asked Questions (FAQ)

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