Find the area under the curve y = 1/(3 x^3) from x = 1 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for x ≥ 1.
a) t=10
b)t=100
c) Total area

Question

Find the area under the curve y = 1/(3 x^3) from x = 1 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for x ≥ 1. 
a) t=10
b)t=100
c) Total area

anonymous · Answer

Area under a curve $$\int\limits_{1}^{t}1/(3x^3)$$
Set t= 10 then solve.$$\int\limits_{1}^{10}1/(3x^3)$$
Set t=100 then solve.$$\int\limits_{1}^{100}1/(3x^3)$$
They are looking for the absolute value of the integrand, if I'm not mistaken, for total area.

So it would look like. Then solve and repeat. $$\int\limits_{1}^{10}|1/(3x^3)|$$

anonymous · Answer

Let me know if you want me to show you how to take the integral by hand.