Integrating for Area: Solving a Geometric Problem

  • Thread starter Thread starter odolwa99
  • Start date Start date
  • Tags Tags
    Areas Integration
odolwa99
Messages
85
Reaction score
0

Homework Statement



Hello. Please refer to attachment for the question. Also, in the attachment, the diagram on the left was included with the question, whereas the diagram on the right is my attempt at representing the enclosed region, asked for in the statement.

Homework Equations





The Attempt at a Solution



Please see attachment.

The final answer, according to the textbook, is 1/4 + ln4.

Thank you.
 

Attachments

  • photo.JPG
    photo.JPG
    24.9 KB · Views: 454
Physics news on Phys.org
Your answer is correct.
 
Your answer looks correct to me, I think it's a book typo.

The only i will say is that when you have integrate 1/x you write x^0 evaluate between 1 and 4, but then you evaluate it between natural logarithm. You shouldn't write x^0. The integral of 1/x is just ln(x).
 
Great. Thanks guys.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top