What is the integral from 4 to 5 of ((e^y)/3)^2 ?

The integral from 4 to 5 of ((e^y)/3)^2 is (e^{10}-e^8)/(18)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 4 to 5 of ((e^y)/3)^2

\int_{4}^{5} (\frac{e ^{y}}{3})^{2} d y

\frac{e ^{10} - e ^{8}}{18}

Decimal

1058.08376 \dots

Solution steps

\int_{4}^{5} (\frac{e ^{y}}{3})^{2} d y

Apply Integration By Parts

: [\frac{1}{9} e^{2 y} y - \int \frac{2}{9} e^{2 y} y d y]_{4}^{5}

= [\frac{1}{9} e^{2 y} y - \int \frac{2}{9} e^{2 y} y d y]_{4}^{5}

\int \frac{2}{9} e^{2 y} y d y = \frac{1}{18} (2 e^{2 y} y - e^{2 y})

= [\frac{1}{9} e^{2 y} y - \frac{1}{18} (2 e^{2 y} y - e^{2 y})]_{4}^{5}

Simplify

[\frac{1}{9} e^{2 y} y - \frac{1}{18} (2 e^{2 y} y - e^{2 y})]_{4}^{5} : [\frac{1}{18} e^{2 y}]_{4}^{5}

= [\frac{1}{18} e^{2 y}]_{4}^{5}

Compute the boundaries:

\frac{e ^{10} - e ^{8}}{18}

= \frac{e ^{10} - e ^{8}}{18}

n = 1 \sum \infty \frac{n ^{4}}{2 ^{n}}

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

\int 10 sin (x) 2 x d x

\frac{d}{d x} (arcsec (x) + arccsc (x))

\frac{x}{x + 3}

What is the integral from 4 to 5 of ((e^y)/3)^2 ?
The integral from 4 to 5 of ((e^y)/3)^2 is (e^{10}-e^8)/(18)