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

Reading that as

$F(x)=\displaystyle\int_1^{3x}(\ln t)^2\,\mathrm dt$

By the fundamental theorem of calculus, the first derivative is

$F'(x)=3(\ln(3x))^2$

and so the second derivative would be

$F''(x)=\dfrac{6\ln(3x)}x$

which means

$F''(1)=6\ln3$

Answer 2

Answer: answer is 6

Step-by-step explanation:

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