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Kris
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How do I find the derivative of the integral of ln(t^2 + 1)dt from 0 to x^2?
The answer is 2xln(x^4 + 1)
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- ecapS trebliHLv 69 years agoFavorite Answer
Given any continuous function f, define F(x) = Int_(0,x) f(t) dt
Then F'(x) = f(x) : fundamental theorem of calculus
By the chain rule, d/dx F(x^2) = F'(x^2) d/dx (x^2) = F'(x^2) 2x = f(x^2) 2x
In this case f(t) = ln(t^2 + 1)
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