Answer:
Step-by-step explanation:
Given the definite integral , we to evaluate it. Using integration by substitution method.
Let u = 1-2x⁵ ...1
du/dx = -10x⁴
dx = du/-10x⁴.... 2
Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;
substitute u = 1-2x⁵ into the result
Hence
Answer:
The result of the integration is
Step-by-step explanation:
Integration of a power of x:
The integration of a power of x is:
In this question:
. So
The result of the integration is
Answer:
Step-by-step explanation:
The logistic differential equation is as follows:
In this problem, we have that:
, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.
At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.
This means that when
. With this, we can find r, that is, the growth rate,
So
So the differential equation is: