Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Inverse Trig Calc BC Integration

  1. Mar 4, 2010 #1
    An interesting AP Calculus BC problem I have not been able to solve.

    1. The problem statement, all variables and given/known data
    "If the substitution [tex]\sqrt(x)=sin(y)[/tex] is made in the integrand of [tex]\int\frac{\sqrt(x)*dx}{\sqrt(1-x)}[/tex] , the resulting integral is ... [5 choices are given]

    (A) integral(0,1/2,(sin(y))^2,dy)
    (B) 2*integral(0,1/2,(sin(y))^2/cos(y),dy)
    (C) 2*integral(0,pi/4,(sin(y))^2,dy)
    (D) integral(0,pi/4,(sin(y))^2,dy)
    (E) 2*integral(0,pi/6,(sin(y))^2/cos(y),dy)

    2. Relevant equations

    3. The attempt at a solution
    Constructing a triangle yields a few values where 1 is the hypotenuse, sqrt(x) is opposite angle y and sqrt(1-x) is adjacent to y.

    The attempt was trigonometric substitution in the form of integral(sec(y)*sin(y)) which yields tangent y. Unfortunately, I do not know how to change the limits of integration and none of the answers are similar to the integral of tan(y).

    Last edited: Mar 4, 2010
  2. jcsd
  3. Mar 4, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Your substitution is x=sin(y)^2. One of those options is correct. How did you get sec(y)*sin(y)? That's not right.
  4. Mar 5, 2010 #3
    I constructed a triangle using the given information. The sin(y) as in the opposite leg over the hypotenuse is equal to sqrt(x)/1
  5. Mar 5, 2010 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You forgot about the dx. You need to write the integral in terms of dy.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook