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Area between two functions

  1. Jan 22, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the area of the region enclosed between y=4sin(x) and y=3cos(x) from x=0 to x=0.3π.

    2. Relevant equations



    3. The attempt at a solution

    So I know how to do most of this question, the area i am stuck on is finding the intersection point between the two functions, since i know you must have two different areas and then add them to find the total area.

    I am looking to find this intersection point without a calculator.

    I tried to equate 4sinx=3cosx, changing this to 3/4=sinx/cosx, then tanx=3/4. This gets me nowhere though, can anyone help?
     
  2. jcsd
  3. Jan 22, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    I'm not sure why you are trying to pull this off without a calculator, but if tan(x)=3/4 then x=arctan(3/4). So you've found the intersection. The integral from 0 to arctan(3/4) actually comes out pretty neatly. Doing the integral from arctan(3/4) to 3*pi/10 can also be done if you are ok with things like cos(3*pi/10) and sin(3*pi/10) appearing in the final answer. At that point I'd use a calculator if you want an actual number.
     
    Last edited: Jan 22, 2013
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