How would I set this up in my calculator?
Let F(x)=∫ ln(t^2) dt where a= 1 and b=3x . Use your calculator to find F"(1).
I set it up and I got way the wrong answer. I got 2ln(1)=0
why not doing it the actual way ????
∫ ln(t^2) dt
= t ln(t^2) - 2t | from ??????
you have a = 1 to b = 3x
are a and b the lower and upper values ?
if so,
= 3x ln (9x^2) - 6x - (0 - 2)
= .....
I don't know because that's what the question says. Thanks
Yes and b are the lower and upper and I plugged in my value of 1 and got 2.59 but that's not one of my answers. My options are
12
6
4
1/9
It's asking for the second derivative. The first derivative is ln(t^2) evaluated at 3x; you need to differentiate again to get the second derivative.
To set up this integral in your calculator, you need to use the appropriate syntax and function for integration.
The function you are integrating is ln(t^2), and the integral is taken over the interval from a=1 to b=3x. In this case, you want to find F"(1), which represents the second derivative of the integral with respect to x evaluated at x=1.
Here's how you can set it up in your calculator:
1. Open your calculator and enter the integral function: ∫(ln(t^2),t,a,b). Make sure to use the appropriate syntax for the integral function in your calculator.
2. Replace the variables in the integral with the given values: ∫(ln(t^2),t,1,3x).
3. Differentiate this integral twice with respect to x to find the second derivative, F"(x). You can use the differentiation feature of your calculator to do this.
4. Evaluate the second derivative at x=1 to find F"(1) by substituting x=1 into the differentiated expression.
It seems like you might have made a mistake while evaluating the integral, as ln(1^2) is actually equal to 0. However, it's important to note that the result you obtained, 2ln(1) = 0, is not the correct answer for the original problem. Make sure to set up and evaluate the integral correctly using the steps above to get the accurate solution.