Answer:
t = 10
[tex]A = 32496.75[/tex]
t = 100
[tex]A = 324999996.8[/tex]
t = 1000
[tex]A=3.25\times 10^{12}[/tex]
Step-by-step explanation:
The area under the curve is calculated by using the following definite integral:
[tex]A = \int\limits^t_ {1} \,{13\cdot x^{3}} dx[/tex]
[tex]A = 13 \int\limits^t_1 {x^{3}} \, dx[/tex]
[tex]A = \frac{13}{4}\cdot (t^{4}-1)[/tex]
Evaluated areas are presented below:
t = 10
[tex]A = 32496.75[/tex]
t = 100
[tex]A = 324999996.8[/tex]
t = 1000
[tex]A=3.25\times 10^{12}[/tex]
