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)=\frac{6\ln(3x)}x`

which means


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

Answer 2

Answer: answer is 6

Explanation:

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