Integration Help: Struggling with Distance Qn

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In summary, the conversation discusses difficulties with integration and finding the boundary conditions for a given question. The expert suggests integrating the given expression and solving for the constant, and provides steps for solving the second question.
  • #1
jwright13
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I’ve always struggled with integration and I don’t know how to do this question, I’m not sure what I’m being asked to calculate. I tried to calculate this as a definite integral but there is no boundary conditions for the distance the object has traveled which is confusing any help would be appreciated thanks! ( it is the bottom question on the pic)
 

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  • #2
I think you are asking for the first one so integrate the above whole expression and you will get $s= 10t^2 + 2/3 t^3 + c$ now calculate c by putting given values of s and t.
 
  • #3
DaalChawal said:
I think you are asking for the first one so integrate the above whole expression and you will get $s= 10t^2 + 2/3 t^3 + c$ now calculate c by putting given values of s and t.
Thank you! this helped a lot, do u have any idea with the second question? I struggle with understanding integration any help is great thanks!
 
  • #4
In the second question, you have to do exactly the same as the first one. Calculate Work it will come out to be $W= 2e^{2x} +c$ now put the values given you will get $W= 2e^{2x} + 6$
 
  • #5
DaalChawal said:
In the second question, you have to do exactly the same as the first one. Calculate Work it will come out to be $W= 2e^{2x} +c$ now put the values given you will get $W= 2e^{2x} + 6$
Thank you so much! this really helped
 

1. What is integration?

Integration is a mathematical concept that involves finding the area under a curve. It is used to solve problems involving rates of change, such as finding the displacement of an object over time or the total amount of a substance produced in a chemical reaction.

2. What is the purpose of integration?

The purpose of integration is to find the exact value of the area under a curve. This can be useful in a variety of real-world applications, such as in physics, economics, and engineering.

3. What is the difference between definite and indefinite integration?

Definite integration involves finding the area under a curve between two specific points, while indefinite integration involves finding the general solution to an integration problem without specific limits.

4. How do I solve integration problems?

To solve an integration problem, you must first identify the function to be integrated and determine the appropriate integration technique to use. Then, you can apply the integration rules and solve the problem step by step.

5. What are some common integration techniques?

Some common integration techniques include substitution, integration by parts, partial fractions, and trigonometric substitution. It is important to practice and become familiar with these techniques to solve integration problems efficiently.

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