Question

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

Answer 1

@ganeshie8 @sammixboo any idea how to do this problem?

Answer 2

Hey!

Answer 3

hello

Answer 4

You may use the fundamental theorem of calculus :


If \(F(x) = \int\limits_a^{\color{red}{h(x)}} g(t)\,dt\),
then \(F'(x) = g(\color{red}{h(x)}) * \color{red}{h'(x)}\)

Answer 5

that gives me F'(x) but the question asks for F" so how do I get that?

Answer 6

Yeah, first find F'(x).

Answer 7

\[g(3x) * 3\]

Answer 8

\[\ln(3x)^2 * 3\]

Answer 9

what next?

Answer 10

Looks good. That is F'(x)

Answer 11

\[F'(x) = 3\ln(3x)^2 \]

Answer 12

You must know what to do next

Answer 13

find the derivative of F'x?

Answer 14

Yes. That gives you F''(x) = ( F'(x) )'

Answer 15

then plug in 1 for x to find F"(1)?

Answer 16

That's it!

Answer 17

thank you so much!!!

Answer 18

yw :)