What is the integral from 0 to 2 of pi(e^x)^2 ?

The integral from 0 to 2 of pi(e^x)^2 is (pi(e^4-1))/2

Popular >

integral from 0 to 2 of pi(e^x)^2

\int_{0}^{2} π (e^{x})^{2} d x

\frac{π ( e ^{4} - 1 )}{2}

Decimal Notation

84.19177 \dots

Solution steps

\int_{0}^{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_{0}^{2} (e^{x})^{2} d x

Apply u-substitution

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

= π \cdot \int_{1}^{e^{2}} u d u

Apply the Power Rule

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

= π [\frac{u ^{2}}{2}]_{1}^{e^{2}}

Compute the boundaries:

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

= π (\frac{e ^{4}}{2} - \frac{1}{2})

Simplify

= \frac{π ( e ^{4} - 1 )}{2}

y = x - cos^{2} (x)

y = \frac{15}{x ^{3} + 2 x}, 1, 2

\frac{\partial}{\partial x} (\frac{x}{x + \frac{y}{x}})

lo g_{10} (4) (x - 1)

\frac{d}{d x} (e^{c o s (x^{3})})

What is the integral from 0 to 2 of pi(e^x)^2 ?
The integral from 0 to 2 of pi(e^x)^2 is (pi(e^4-1))/2