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

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

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integral from-1 to 1 of pi(e^x)^2

\int_{- 1}^{1} π (e^{x})^{2} d x

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

Decimal Notation

11.39411 \dots

Solution steps

\int_{- 1}^{1} 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_{- 1}^{1} (e^{x})^{2} d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

9 x^{l n (9 x)}

h (x) = e^{x} + x^{5}

x \to \frac{5}{2} lim (x^{2} + 2 x + 4)

\int cos (\frac{3 x}{2}) d x

x \to - 3 lim (\frac{1}{x - 3})

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