Answer:
[tex]A=\frac{17}{4}[1-t^{-4}][/tex]
A1 = 4.249
A2 = 4.249
A3 = 4.25
Step-by-step explanation:
You have the following function:
[tex]y(x)=\frac{17}{x^3}[/tex]
To find the area under the curve, between x=1 and x=t, you integrate y(x):
[tex]A=\int y(x)dx=\int_1^t\frac{17}{x^3}dx=17\int_1^tx^{-3}dx\\\\A=17(\frac{x^{-4}}{-4})|_1^t=\frac{17}{4}[1-t^{-4}][/tex]
For t = 10
[tex]A_1=\frac{17}{4}[1-(10)^{-4}]=4.249[/tex]
t = 100
[tex]A_2=\frac{17}{4}[1-(100)^{-4}]=4.249[/tex]
t = 1000
[tex]A_2=\frac{17}{4}[1-(1000)^{-4}]=4.25[/tex]
