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# Maths differentiating/integrating e to the power of something

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1. If you differentiate 0.5e^t, you get 0.5e^t and if you integrate it you get 0.5e^t +c. If the limits are 0 to t, how do you find out c. I know the answer is -1 but why?
Thanks, Lauren
2. (Original post by Lauren_F1)
If you differentiate 0.5e^t, you get 0.5e^t and if you integrate it you get 0.5e^t +c. If the limits are 0 to t, how do you find out c. I know the answer is -1 but why?
Thanks, Lauren
If you do integration between limits, the c's cancel because you are finding the difference between two integrations.

One evaluated at the upper limit and the other at the lower limit. The value of -1 comes from the value of e^0 in the lower limit.

Working out c comes from a situation in which you have a boundary condition such as (say) f(t)=5 when t=0 which will lead to some value of c (4 in this case)

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