What is the integral from-2 to 2 of pi(e^x)^2 ?

The integral from-2 to 2 of pi(e^x)^2 is pi((e^4)/2-1/(2e^4))

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integral from-2 to 2 of pi(e^x)^2

\int_{- 2}^{2} π (e^{x})^{2} d x

π (\frac{e ^{4}}{2} - \frac{1}{2 e ^{4}})

Decimal Notation

85.73380 \dots

Solution steps

\int_{- 2}^{2} π (e^{x})^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{- 2}^{2} (e^{x})^{2} d x

Apply u-substitution

: \int_{\frac{1}{e ^{2}}}^{e^{2}} u d u

= π \cdot \int_{\frac{1}{e ^{2}}}^{e^{2}} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{\frac{1}{e ^{2}}}^{e^{2}}

= π [\frac{u ^{2}}{2}]_{\frac{1}{e ^{2}}}^{e^{2}}

Compute the boundaries:

\frac{e ^{4}}{2} - \frac{1}{2 e ^{4}}

= π (\frac{e ^{4}}{2} - \frac{1}{2 e ^{4}})

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What is the integral from-2 to 2 of pi(e^x)^2 ?
The integral from-2 to 2 of pi(e^x)^2 is pi((e^4)/2-1/(2e^4))