Don't definite Integrals find area?

In summary, the conversation is about finding the area of a region bounded by a function using both Riemann sums and definite integrals. The person initially had trouble with their definite integral not matching the Riemann sum, but eventually realized their mistake and got the correct answer. They thank someone named Roco for their help.
  • #1
lLovePhysics
169
0
I'm confused here.. My definite integral doesn't match by Riemman Sum... and it should right? I think that I have not integrated correctly. Can someone help me spot the problem? Thanks.

Find the Area of the region bounded by:
[tex]f(x)=5-x^2[/tex] , [-2, 1]

Using the Riemma Sum idea (limit of the sum of rectangles as the number of rectangles approaches infinity), I got 12 units^2 as my area, which is correct.

However, using definite integrals and the Fundamental Theorem of Calculus, I get:

[tex]\int_{-2}^{1} (5-x^2)dx}[/tex]

[tex]=-\frac{x^3}{3}\biggl] ^{1}_{-2}[/tex]

Which equals -3 ?
 
Physics news on Phys.org
  • #2
5x - 1\3 * x^3
 
  • #3
rocophysics said:
5x - 1\3 * x^3

Noooo.. I can't believe I made another stupid mistake! Thanks Roco
 

1. What is a definite integral?

A definite integral is a mathematical concept used to find the area under a curve between two specified points on a graph. It is represented as ∫f(x)dx, where f(x) is the function and dx represents an infinitesimal change in the x-axis.

2. How is a definite integral different from an indefinite integral?

A definite integral has specified limits of integration, while an indefinite integral does not. This means that a definite integral will give a specific numerical value, while an indefinite integral will give a function.

3. How does a definite integral find the area under a curve?

A definite integral finds the area under a curve by dividing the region into infinitely small rectangles, calculating the area of each rectangle, and then summing up all the areas to find the total area under the curve.

4. What are the applications of definite integrals in science?

Definite integrals are used in various fields of science, including physics, chemistry, and engineering. They are used to calculate quantities such as displacement, velocity, acceleration, and work, which are essential in understanding the behavior of physical systems.

5. Can definite integrals be used for non-linear functions?

Yes, definite integrals can be used for non-linear functions. In fact, they are often used to find the area under curves that are not linear. This is because definite integrals can handle any type of function, as long as the limits of integration are properly defined.

Similar threads

  • Calculus and Beyond Homework Help
Replies
14
Views
191
  • Calculus and Beyond Homework Help
Replies
6
Views
930
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
243
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
946
  • Calculus and Beyond Homework Help
Replies
10
Views
415
  • Calculus and Beyond Homework Help
Replies
8
Views
753
  • Calculus and Beyond Homework Help
Replies
9
Views
745
  • Calculus and Beyond Homework Help
Replies
5
Views
324
Back
Top