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Posted by on Thursday, December 10, 2009 at 10:31am.

For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral.

INT((4x^2-3)^1.5) dx x=?

  • Calculus - , Thursday, December 10, 2009 at 11:40am

    u = 4x^2 -3
    (1/8)du = x dx
    (1/8)INT u^(3/2) du
    (1/8)(2/5)u^(5/2)
    (1/20)(4x^2 -3)^(5/2)

    I don't see why they demand a trigonometric solution. This seems like the logical one to use.

  • Calculus - , Thursday, December 10, 2009 at 4:07pm

    No it is required to use a trignometric substitution. x cannot be a variable in the final answer

  • Calculus - , Thursday, December 10, 2009 at 5:51pm

    you can do like this:
    (4x^2-3)^1.5 = (4x^2-3).sq(4x^2-3)dx
    Let 2x = Sq3.sec(det)
    so, 4x^2 -3 = 3.sec^2(det)-3
    = 3.tan^2(det)
    new INT= INt(3^1.5tan^3(det)d(det)
    Use Pythagore to solve the relation between x and the angle det.

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