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Kris
Lv 5
Kris asked in Science & MathematicsMathematics · 9 years ago

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)

1 Answer

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  • 9 years ago
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    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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