Finding the Derivative of an Integral: Explanation Needed

In summary, the conversation involves a student seeking help with taking the derivative of an integral and finding the correct answer. They are having trouble understanding where the constants in the solution come from. Another person asks for clarification on whether the integral is being differentiated or if it is the integral of the integral.
  • #1
juice34
1. Homework Statement
Can someone help me take the derivative of the integral
u(1/r)((d/dr)[(r)(dV/dr)])=P


2. Homework Equations



3. The Attempt at a Solution
my attempt yields V=(Pr^2)/(2u)+C(1), which is not right. The actual answer is V=(Pr^2)/4u+C(1)ln(r)+C(2). I am having trouble finding out where the 4 and everything else comes from could someone please explain to me what is going on. Thank YOU
 
Physics news on Phys.org
  • #2
When you first integrated, did you include your constant? If not, that might explain why you lacked the extra term upon the second integration.
 
  • #3
You want to find
[tex]\frac{d}{dx}\int u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}dr[/tex]?
That, of course, is equal to
[tex]u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}[/tex]?

Or do you mean the integral of that integral?
 

1. What is the derivative of an integral?

The derivative of an integral is the original function from which the integral was derived. It represents the rate of change of the integral function at a specific point.

2. How do you find the derivative of an integral?

The derivative of an integral can be found by using the Fundamental Theorem of Calculus, which states that the derivative of an integral is equal to the integrand evaluated at the upper limit of the integral.

3. Why is the derivative of an integral important?

The derivative of an integral is important because it allows us to calculate the instantaneous rate of change of a quantity, which is useful in many areas such as physics, economics, and engineering.

4. Can the derivative of an integral be negative?

Yes, the derivative of an integral can be negative. This means that the original function is decreasing at that specific point.

5. What is the relationship between the derivative and integral?

The derivative and integral are inverse operations of each other. The derivative gives the rate of change of a function, while the integral gives the accumulated change over an interval. They are connected by the Fundamental Theorem of Calculus.

Similar threads

B Integration by parts of inverse sine, a solved exercise, some doubts...
    • Calculus
Replies
4
Views
910
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
    • Calculus
Replies
1
Views
2K
B Integration by Parts, an introduction I get confused with
    • Calculus
Replies
2
Views
931
I Express the limit as a definite integral
    • Calculus
Replies
16
Views
2K
B Having trouble deriving the volume of an elliptical ring toroid
    • Calculus
Replies
4
Views
348
I Did Math DF's integral calculator make a glaring mistake?
    • Calculus
Replies
8
Views
176
MHB Change of Variables in Multiple Integrals
    • Calculus
Replies
2
Views
1K
B Why is this definite integral a single number?
    • Calculus
Replies
20
Views
2K
I Gaussian integral by differentiating under the integral sign
    • Calculus
Replies
19
Views
3K
I Finding the derivative of a characteristic function
    • Calculus
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top