How would you solve this integral?

S

sigma

Junior Member
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Feb 19, 2006
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Just had this on a quiz and was kinda stumped. Now I have worked with definite integrals when you have an "x" on the top and a number on the bottom of the integral; you just subsistute the x into the "t" and apply the chain rule for the x value but this question used an "x" on the bottom and a number on the top so I don't know if that same rule applies. I did plug in x-squared into the "t's" for the function but now I'm thinking it has to be negated because the x is in the bottom. Can somebody help me out? Here's the question, I'm not quite sure if that is how it was worded exactly, it might have been find f'(x) instead of finding f(x) but I just want to know how to solve the integral part with an "x" on the bottom and a number on the top.
\(\displaystyle \
\L\
{\rm Find f(x) if f '(x) = }\int_{x^2 }^4 {e^{t^3 } - t^3 } dt
\\)

Edit by TKHunny - Differential Corrected
 
If indeed it were \(\displaystyle \
\L\
{\rm Find f'(x) if f(x) = }\int_{x^2 }^4 {e^{t^3 } - t^3 } dt
\\) then \(\displaystyle \L
f'(x) = - \left[ {e^{\left( {x^2 } \right)^3 } - \left( {x^2 } \right)^3 } \right]\left( {2x} \right)\).

Note the minus: because x<SUP>2</sup> is the lower limit.
 
I knew it. The only mistake I made was not putting the minus sign there. Thanks allot!
 
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