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Applications of Integration (simple problem, but not getting right answer)

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Applications of Integration: y=x^2+1 and y=sq root(1-x^2)
    the graph (shown in the book) shows two curves from the two given equations (one obivously positive and the other negative) the shaded area is in between the two curves

    the bounds are x=1 and the shaded area is only in quadrant I, so i assume x=0

    2. Relevant equations
    ∫[a,b] f(x)-g(x)dx

    3. The attempt at a solution

    the bounds i chose are [0,1]
    ∫x^2+1 -(sqrt(1-x^2) dx
    1/3*x^3 + x -(2/3*(1-x^2)^(3/2) * (-1/2x)) |1 to 0
    1/3*x^3 + x (1/(3x))(1-x^2)^(3/2)) |1 to 0

    1/3*(1)^3 + (1) +(1/(3(1)))(1-(1)^2)^(3/2)) -[1/3*(0)^3 + (0) +(1/(3(0)))(1-(0)^2)^(3/2))]

    simply 1/3 + 1 + (1/3)(0) - [0 + 0+ (1/0)]

    the back of the book speakeths: 4/3 - pi/4
  2. jcsd
  3. Oct 16, 2011 #2


    Staff: Mentor

    Your work for the integral of the radical is incorrect. The standard way of doing this type of integral is using a trig substitution.
  4. Oct 16, 2011 #3
    duh dude... I knew that...

    lol! thanks. That helped answer my next few questions. Thanks!
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