Definite Integration: 9_0 c/x^3 dx = (3/8)c

In summary, the conversation discusses the integration of c/x^3 and the correct answer being (3/8)c. The conversation also mentions the importance of writing fractions in the form of cx^-n for simplification.
  • #1
cd246
30
0

Homework Statement


integration 9_0 c/x^3 dx. the answer is (3/8)c.

Homework Equations


just distrib. then plug in the #'s

The Attempt at a Solution


=cx^-3
= (cx^-2)/-2=c/-2x^2
I know it has something to do with distribution.
 
Last edited:
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  • #2
I assume your problem statement is supposed to represent this(please confirm):

[tex]\int^9_0 \frac{c}{x^3}dx[/tex]

If this is the case, I agree with your answer. When I evaluate the integral at the bounds I do not get the answer you stated. I get -c/162 as an answer. Are you sure that is correct?
 
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  • #3
My apologies, it is 2_1 not 9_0
 
  • #4
cd246 said:
My apologies, it is 2_1 not 9_0

Ahh if that is the case, then I do get (3/8)c as the answer. Were the bounds your problem, or is there something else?
 
  • #5
that was pretty much it. did u put x^3 on top? or did you left the x^3 on the bottom? Because i believe that was my problem on this one.
 
  • #6
cd246 said:
that was pretty much it. did u put x^3 on top? or did you left the x^3 on the bottom? Because i believe that was my problem on this one.

I think it is good practice to write any fraction of c/x^n as cx^-n. I think it makes many problems look less complicated. So, yes, if this is what you mean, I did "put the x^3 on top."
 
  • #7
ok i got it now. thanx
 
  • #8
Your Welcome!
 

1. What is definite integration?

Definite integration is a mathematical process used to find the area under a curve between two specific points on a graph. It is represented by the symbol ∫ and involves finding the antiderivative of a function.

2. How is definite integration different from indefinite integration?

Definite integration involves finding a specific numeric value for the area under a curve, while indefinite integration involves finding a general formula for the antiderivative of a function. In definite integration, the limits of integration are specified, while in indefinite integration, they are not.

3. What does the notation "c/x^3 dx" mean in definite integration?

The notation "c/x^3 dx" represents the function being integrated. In this case, it is a function of x, where c is a constant and x^3 is the variable of integration. The "dx" indicates that the integral is with respect to x.

4. How is the value of (3/8)c obtained in the definite integration of "9_0 c/x^3 dx = (3/8)c"?

In this case, the value of (3/8)c is obtained by plugging in the limits of integration (9 and 0) into the antiderivative, which is (c/x^2). This gives us (3/8)c as the final result.

5. What is the significance of definite integration in science?

Definite integration is used in many areas of science to calculate important quantities such as mass, volume, and work. It also plays a crucial role in solving differential equations, which are used to model many physical phenomena in science.

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