MHB Integration Help: Struggling with Distance Qn

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The discussion revolves around difficulties with integration, specifically calculating distance and work from given expressions. The first user expressed confusion over a distance question without boundary conditions, and received guidance on integrating the expression to find the distance function, including how to determine the constant 'c' using provided values. The second question also required integration to calculate work, with a similar approach suggested, resulting in a specific expression for work. The user found the assistance helpful and requested further help on the second question, which was also addressed effectively. Overall, the thread highlights the importance of understanding integration techniques in solving physics-related problems.
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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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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.
 
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!
 
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 $W= 2e^{2x} + 6$
 
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
 

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