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

so, is

F(x) = ∫[1,3x] ln(t^2) dt
or
F(x) = ∫[1,3x] (ln t)^2 dt
?

Either way,
f(x) = F'(x) = ln(3x)^2 * 3
or
f(x) = F'(x) = (ln 3x)^2 * 3

And F" = f'

Recall that the 2nd Fundamental Theorem of Calculus says that if

F(x) = ∫[a,g(x)] f(t) dt
then
F'(x) = f(g(x)) * g'(x)

Answer 2

it's 6 just did the test.

Answer 3

what test??? please help