Answer:
The definite integral expressing the total quantity of oil, 'V', which leaks out of the tanker in the first hour is given as follows;
Step-by-step explanation:
From the question, we have;
The rate at which oil leaks out of the tanker, r = f(t)
The unit of the oil leak = Liters per minute
The unit of t = Minutes
Therefore, we have;
The definite integral expressing the total quantity, 'V', of oil which leaks out of the tanker in the first hour is given as follows;
Therefore, we have;
Answer:
-14.
Step-by-step explanation:
- because of the -14x^6
I'm not sure but your answer might be 100 but I'm not sure
Answer:
INF for first while D for second
Step-by-step explanation:
Ok I think I read that integral with lower limit 1 and upper limit infinity
where the integrand is ln(x)*x^2
integrate(ln(x)*x^2)
=x^3/3 *ln(x)- integrate(x^3/3 *1/x)
Let's simplify
=x^3/3 *ln(x)-integrate(x^2/3)
=x^3/3*ln(x)-1/3*x^3/3
=x^3/3* ln(x)-x^3/9+C
Now apply the limits of integration where z goes to infinity
[z^3/3*ln(z)-z^3/9]-[1^3/3*ln(1)-1^3/9]
[z^3/3*ln(z)-z^3/9]- (1/9)
focuse on the part involving z... for now
z^3/9[ 3ln(z)-1]
Both parts are getting positive large for positive large values of z
So the integral diverges to infinity (INF)
By the integral test... the sum also diverges (D)
Answer:
81π ft³
Step-by-step explanation:
If the diameter is 6 ft, the radius is 3 ft.
The volume is V = (area of base)(height).
Here, V = (π[3 ft]²)(9 ft) = 81π ft³