Having a problem in steps while solving integrals

  • Thread starter prakhargupta3301
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In summary, the homework equations state that x_x is a function of x and k, and that a=dv/dt and v=dx/dt. The attempted solution is that a=dv/dt⋅dt/dx, and that v=dx/dt when v is limited to a range between 2u and u.
  • #1
prakhargupta3301
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1

Homework Statement


The problem is attached. I'm new to these problems (calculus).
I'm not getting my answer as any of the options. I need your help to know whether me or the slide is wrong.
?temp_hash=12720349bd7b2b5fb6e9c4da92df3e15.png

Homework Equations


x_x[/B]

The Attempt at a Solution


IMG_20180619_034801.jpg

Thank you for reading.
 

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  • #2
What is ∫v.dv?
 
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  • #3
The slide is wrong in that x is not constant, k is constant. Your formulation is correct up to ∫ v dv as pointed out by haruspex.
 
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  • #4
haruspex said:
What is ∫v.dv?
It is an equation to solve kinematic equations.
a=dv/dt 1
v=dx/dt 2
Divide 1 by 2
a/v= dv/dt⋅dt/dx
a/v=dv/dx
a⋅dx=v⋅dv
Integrate LHS and RHS and you get 3rd equation of motion:
0x∫a⋅dx=uv∫v⋅dv
a⋅x0x=v2|uv
ax-0=v2/2-u2/2
2ax=v2-u2
 
  • #5
Dr Dr news said:
The slide is wrong in that x is not constant, k is constant. Your formulation is correct up to ∫ v dv as pointed out by haruspex.
So, am I correct or not ? This was quite an ambiguous reply..
If not, can you point out the mistake clearly and correction. Please?
 
  • #6
Your LHS (2/3) k^2 x^(3/2) is OK the RHS as you have corrected is v^2 / 2 with an upper limit of 2u and a lower limit of u.
 
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  • #7
prakhargupta3301 said:
=uv∫v⋅dv...=v2|uv
Quite so, but that does not seem to be what you wrote in your attachment in post #1. I do not see a 2 there.
 
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  • #8
Dr Dr news said:
Your LHS (2/3) k^2 x^(3/2) is OK the RHS as you have corrected is v^2 / 2 with an upper limit of 2u and a lower limit of u.
haruspex said:
Quite so, but that does not seem to be what you wrote in your attachment in post #1. I do not see a 2 there.
So, I was incorrect in believing v to be a constant! Silly me. (I pondered over this single question for an hour and didn't get any sleep last night xD)
Thank you both for helping me. Have a great day/night.
 

1. What is the first step in solving integrals?

The first step in solving integrals is to identify the function that needs to be integrated. This function is often denoted as f(x) or g(x). It is important to understand the function and its characteristics before proceeding to the next steps.

2. How do I determine the limits of integration?

The limits of integration are determined by the range of values for the independent variable, which is typically denoted as x. These limits can be given in the integral expression or can be inferred from the context of the problem. It is important to correctly identify the limits of integration before proceeding with the integration process.

3. What are the different methods for solving integrals?

There are several methods for solving integrals, including substitution, integration by parts, partial fractions, and trigonometric substitution. Each method is useful for different types of functions and can be chosen based on the complexity of the integral.

4. How do I check if my solution for an integral is correct?

To check the correctness of your solution for an integral, you can differentiate the result and see if it matches the original function that was being integrated. You can also use online tools or calculators to verify your answer.

5. What should I do if I get stuck while solving an integral?

If you get stuck while solving an integral, try going back to the first step and carefully reviewing the function and the limits of integration. You can also try using a different method or consult a textbook or online resources for help. It is important to carefully follow the steps and not make any careless mistakes.

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