Question

F of x equals the integral from 1 to x of the natural logarithm of t squared. Use your calculator to find F ′(3).

Answer 1

https://gyazo.com/3d3327245c9230958f68094e39259155

Answer 2

@jim_thompson5910 I selected that by mistake, I am not sure what to do here.

Answer 3

@ganeshie8 how'd you get that? I got 13.2 plugging in 3

Answer 4

By the Fundamental Theorem of Calculus (FTC)


if
\[\Large F(x) = \int_{a}^{x}f(t)dt\]
then
\[\Large F \ ' (x) = f(x)\]

Answer 5

**
\(F(x) = \int\limits_{1}^x\ln (t^2)\,dt\)

\(F'(x) = \ln(x^2)*(x)' = \ln(x^2)\)

plugin \(x=3\)

Answer 6

A bit more generally :
\[\dfrac{d}{d\color{red}{x}}\int\limits_a^{g(\color{red}{x})} f(t) \,dt = f(g(x))*g'(x)\]

Answer 7

Ok, got it. Thanks to you both.

Answer 8

np