Answer:
Step-by-step explanation:
given is a function as
[tex]y=\frac{27}{x^3}[/tex]
We are to find the area form x=1 to x=t
The curve from x=1 lies in the I quadratnt.
So area above x axis is to be calculated
Area = [tex]\int\limits^t_1 {\frac{27}{x^3} } \, dx \\=\frac{-27}{2x^2} \\= \frac{-27}{2t^2}-\frac{-27}{2}\\=\frac{27}{2}(1-\frac{1}{t^2} )[/tex]
a) When t =10,
area = [tex]\frac{27}{2} (1-\frac{1}{10^2} )\\= 13.365[/tex]
b) t=100
area = [tex]\frac{27}{2} (1-\frac{1}{100^2} )\\= 13.49865[/tex]
c) t=10000
area = [tex]\frac{27}{2} (1-\frac{1}{10000^2} )\\= 13.5[/tex]
