Answer:
0.333[tex]\pi[/tex] units³
Step-by-step explanation:
Think process:
The equation is given as y = [tex]e^{-3x}[/tex]
Let, y = f (x)
Therefore, [tex]f (x) = e^{-3x}[/tex]
We know that the limits are y-axis and x= 3
Y-axis: x= 0
then limits are given as x= 0 and x = 3
Integrating gives:
[tex]\int\limits^3_0 {e^{-3x} } \, dx[/tex] = [tex]\frac{-1}{3}e^{-3x}[/tex] + C
calculating from x= 0 to x = 3, we know volume is given by [tex]\pi \int\limits^a_b {f(x)} \, dx[/tex]
= [tex]\pi[/tex][ [tex]\frac{-1}{3} e^{-9} - (\frac{-1}{3} e^{0})[/tex]]
= [tex]\pi[/tex][0.000041136 + 1/3]
= 0.333[tex]\pi[/tex] units³
