• Support PF! Buy your school textbooks, materials and every day products Here!

Weird integral question

  • Thread starter Emethyst
  • Start date
  • #1
118
0

Homework Statement


Find the integral of sqrt(9-x^2) over [0,3]. You will not be able to find an antiderivative, so instead interpret the definite integral as the area of a region and compute the area geometrically (I haven't reached integration by substitution and integration by parts in class yet).



Homework Equations


The part i'm lost on



The Attempt at a Solution


This question has me stumped. I tried using both riemann sums and the trapezoid method but this didn't get me anywhere, as the answer is supposed to be 9pi/4. It is only out of 1 mark, so I know it can't be that difficult, but i'm still lost over it. Any pointers in the right direction here would be greatly appreciated. Thanks in advance.
 

Answers and Replies

  • #2
Pyrrhus
Homework Helper
2,178
1
Are you familiar with this geometry figure [itex] y^2 + x^2 = 3^2 [/itex] ? Now consider what the square root does to this relation? (this is not a function), but when [itex] y = \sqrt{3^2 - x^2} [/itex] what happens? (think in terms of Real value [itex] \sqrt{x} [/itex] function)
 
Last edited:
  • #3
16
0

Homework Statement


Find the integral of sqrt(9-x^2) over [0,3]. You will not be able to find an antiderivative, so instead interpret the definite integral as the area of a region and compute the area geometrically (I haven't reached integration by substitution and integration by parts in class yet).



Homework Equations


The part i'm lost on



The Attempt at a Solution


This question has me stumped. I tried using both riemann sums and the trapezoid method but this didn't get me anywhere, as the answer is supposed to be 9pi/4. It is only out of 1 mark, so I know it can't be that difficult, but i'm still lost over it. Any pointers in the right direction here would be greatly appreciated. Thanks in advance.
Try downloading the program Geogebra (Web Start) - it's free math software, then let it draw the graph of this "weird" thing. You'll probably see what the answer is..
 
  • #4
118
0
No I have not heard of that geometric figure before, but I do know that the square root prevents the function from crossing zero and becoming a negative number, and in a sense resembles half of a horizontal parabola. Now for the obvious question, how does that help me? :tongue:
 
  • #5
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,098
129
Okay, how about

x2 + y2 = r2

Is that figure more familiar to you?
 
  • #6
118
0
Ohh it's a circle, I see it now, the radius is 3 so I just need to use the area formula and divide the answer by 4. Thanks for all the help guys :smile:
 

Related Threads for: Weird integral question

  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
6
Views
916
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
2K
Top