1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why can't I do this?

  1. Mar 16, 2004 #1
    Ok, I was thinking today during my calculus class about taking the integral of a function in a different way. Let's assume for a second that we want to find the area between the function and the y axis, on the interval x = [0, 2] of the function y = 2x.

    What I was thinking I could do, is take the integral of y.

    (y^2)/2 then substitute 2x in for y, since y = 2x.

    (2x)^2 / 2

    That would give us the integral between the function and the y axis and we would be able to put in the interval for x.

    But it didn't work... I got the wrong answer? Why doesn't this work? I think it should work.

  2. jcsd
  3. Mar 16, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Because that isn't how integration works?

    Imagine doing the same for differentiation.

    we want to find d/dx of x^2, well, d/dy of y is 1, so putting y=x^2, we get d/dx(x^2)=1

    It just isn't right.

    More formally remember integration is wrt something

    so integral of ydy is not the same as integral of x^2dx when you put x^2=y because the dy and dx are there, and if y=x^2, then dy is not dx - it is 2xdx
  4. Mar 17, 2004 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    y=2x and x ranges between 0 and 2.

    Of course, that's simply a right triangle with base (x-axis) of length 2 and height (y-axis) of length 4: its area is (1/2)(2)(4)= 4.

    You could do this as [tex]\int_0^2(ydx)= \int_0^2(2x)dx= x^2\|_0^2= 4[/tex]

    You could do this as [tex]\int_0^4(xdy)= \int_0^4\frac{y}{2}dy= \frac{y^2}{4}\|_0^4= \frac{16}{4}= 4[/tex]

    Your formula is wrong because you never took into account the "dx" or "dy".
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Why can't I do this?
  1. How do i do this? (Replies: 2)

  2. I just can't get this (Replies: 3)