Respuesta :
The quantity of oil in the first 180 minutes was 62.78 million gallons.
Integration
It is the reverse of differentiation.
Given
An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking out will diminish.
The tanker breaks apart, the oil is leaking out at a rate of R(t).
[tex]\rm R(t) = \dfrac{0.7}{1 + t^2}[/tex], where t is time in minutes.
How much a million gallons of oil will leak out in the first 3 hours after the shipwreck?
Convert the hours into minutes.
1 hours = 60 minutes
3 hours = 180 minutes
Then the quantity of oil in the first 180 minutes will be
V(t) = R(t)
Integrate the function.
[tex]\rm V(t) = \int_0^{180} R(t) dt\\\\V(t) = \int_0^{180} \dfrac{0.7}{1+t^2} dt\\\\V(t) = 0.7 \int_0^{180} \dfrac{1}{1 + t^2}dt\\\\V(t) = 0.7[tan^{-1}t]_0^{180}\\\\V(t) = 0.7 [tan^{-1}180 -tan^{-1}0]\\\\V(t) = 0.7 * 89.682\\\\V(t) = 62.78[/tex]
Thus, the quantity of oil in the first 180 minutes was 62.78 million gallons.
More about the integration link is given below.
https://brainly.com/question/18651211
