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1. The question is "Find f(x) if you are told that f'(x)=10x^4+6x^2+1 and f(1) = 3

I answered it by first integrating to get: 2x^5 + 2x^3 + 0.5^2 + C

Then to find C, I tried putting 1 through what I integrated without C to get 4.25. I know that f(1) = 3, so I did 4.25 - 3 = 1.25, so I put that C = 1.25.

Is that right? There aren't any answers on the worksheets I'm doing. Thanks!
2. (Original post by Astravolt)
The question is "Find f(x) if you are told that f'(x)=10x^4+6x^2+1 and f(1) = 3

I answered it by first integrating to get: 2x^5 + 2x^3 + 0.5^2 + C

Then to find C, I tried putting 1 through what I integrated without C to get 4.25. I know that f(1) = 3, so I did 4.25 - 3 = 1.25, so I put that C = 1.25.

Is that right? There aren't any answers on the worksheets I'm doing. Thanks!
You have the right idea, but you have not integrated the "+ 1" piece correctly. What would you differentiate to end up just with 1?
3. Think you made a mistake when integrating it, there shouldn't be a 0.5^2 as 1 integrated is just x.
Then just put 1 into f(x) -> 2 + 2 + 1 + C = 3, solve for C.
4. (Original post by Astravolt)
f'(x)=10x^4+6x^2+1
I answered it by first integrating to get: 2x^5 + 2x^3 + 0.5^2 + C
? You seem to have integrated a constant (1) as it were the function x. To integrate a constant you just multiply it by x.
To check whether you have integrated correctly you should make sure that you get the original expression when you differentiate your answer.
5. if you integrate a number W then you get Wx
6. I didn't know that you had to multiply by x for a constant, thanks for the help!
7. A constant integrates to just that variable.

The power rule that you're using right now says to add one to exponent and divide by new power.

E.g. integrating 5 dx --> we know 5 = 5x^0 so increasing it becomes 5x/1 = 5x. Apart from that, you're correct.

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