#$&*
Mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
chapter 7 book problems
** **
7.8.13 integral from 5 to 8 of 6/(sqrt (t-5)) dt
7.8.15 integral from -1 to 5 of 1/[(t+1^2)]
** **
In number 13, p < 1 so why does this converge?
In number 15, p > 1 so why does this not converge?
@&
You can find the antiderivative for #13; just let w = t - 5, integrate 6 / sqrt(w), etc..
#15 is probably the integral of (t + 1)^2. This is undefined at t = -1, so using tau to stand for the lower limit of the integral, we have to find the limit as tau -> -1 of the integral from tau to 5.
An antiderivative is -1 / (t + 1). Evaluated at limits tau and 5 we get
-1 / (5 + 1) - (-1 / (tau + 1) )
= -1/6 + 1 / (tau + 1).
As tau -> -1, tau + 1 approaches zero and 1 / (tau + 1) approaches infinity.
Thus the integral diverges.
*@