anonymous
  • anonymous
F of x equals the integral from 1 to x of the natural logarithm of t squared. Use your calculator to find F ′(3).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
https://gyazo.com/3d3327245c9230958f68094e39259155
anonymous
  • anonymous
@jim_thompson5910 I selected that by mistake, I am not sure what to do here.
anonymous
  • anonymous
@ganeshie8 how'd you get that? I got 13.2 plugging in 3

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jim_thompson5910
  • jim_thompson5910
By the Fundamental Theorem of Calculus (FTC) if \[\Large F(x) = \int_{a}^{x}f(t)dt\] then \[\Large F \ ' (x) = f(x)\]
ganeshie8
  • ganeshie8
** \(F(x) = \int\limits_{1}^x\ln (t^2)\,dt\) \(F'(x) = \ln(x^2)*(x)' = \ln(x^2)\) plugin \(x=3\)
ganeshie8
  • ganeshie8
A bit more generally : \[\dfrac{d}{d\color{red}{x}}\int\limits_a^{g(\color{red}{x})} f(t) \,dt = f(g(x))*g'(x)\]
anonymous
  • anonymous
Ok, got it. Thanks to you both.
ganeshie8
  • ganeshie8
np

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