Hello Everyone! Today We are asked to find . We are given two option. First is by evaluating the definite integral itself or we can do numerical approximation using both Trapezoidal and Mid point Rules with sub interval n valued at 10. Since I've figured out that integrating such integral would be a , I just gone on and used the Numerical Approximation way. Everything is well until I am asked to find the error for both and . I know the formula and the value of for the second derivative of the function to use it as a rule to find constant from the formula and . Now I am stuck at how to find K when at interval . Anyone got any idea to find ? Thanks y'all in advance!
Edit: I have an idea on how to solve this one. As we can see, x is bounded in [1,2], and that 1/x would only max out at x=1 since anything more than 1 would make x less so we can conclude that . Since K is the max value of the second derivative, then max value is acquired when 1/x is evaluated at x=1. So that so if we substitute 1 to all 1/x, we get: . Is that the right way to do it?Hehe it is late in the morning and I am still pumped to do this problem!