Question

Consider a solid orientated along the x axis such that its cross-sectional area is given by
A(x) = e^(5 x)
Find the volume of the solid contained between x = 17 and x = 23.

Answer 1

\[\large V = \int\limits_{17}^{23}A(x) dx\]
\[\large = \int\limits_{17}^{23} e^{5x} dx\]

Answer 2

\[\int\limits_{17}^{23}e ^{5x}\]

Answer 3

http://www.wolframalpha.com/input/?i=integrate&a=*C.integrate-_*Calculator.dflt-&f2=e^%285x%29&f=Integral.integrand_e^%285x%29&f3=17&f=Integral.rangestart_17&f4=23&f=Integral.rangeend_23&a=*FVarOpt-_**Integral.variable-.*Integral.rangestart-.*Integral.rangeend--

Answer 4

use substitution
u = 5x
du = 5 dx --> du/5 = dx
\[\large \frac{1}{5}\int\limits_{17}^{23}e^{u} du = \frac{1}{5}(e^{5*23} - e^{5*17})\]