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Math Help - cal 2

  1. #1
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    cal 2

    evaluate the definite intergral with limits squar root of pi and 0 xsin(x^2)dx. give answer in decimal number with four places.

    "" limits 5 and 1 1/square root 2x-1 dx give answer in decimal number with four places.

    "" limits 2 and 0 x/square root 1+2x^2 dx.""
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lay137 View Post
    evaluate the definite intergral with limits squar root of pi and 0 xsin(x^2)dx. give answer in decimal number with four places.
    Do you know the fundamental theorem of calculus?

    Do you recognise what x \sin(x^2) is the derivative of?

    Hint: consider \frac{d}{dx} \cos(x^2).

    RonL
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  3. #3
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    Hello, lay137!

    Exactly where is your difficulty?
    These are all straight Substitution problems . . .


    [int] xsin(x) dx . . . from 0 to √2
    Let: u = x


    [int] dx / √(2x - 1) . . . from 1 to 5
    We have: .[int] (2x - 1)^(-) dx

    Let: u = 2x - 1



    [int] x dx / √(1 + 2x) . . . from 0 to 2
    We have: .[int] (1 + 2x)^(-) (x dx)

    Let: u = 1 + 2x

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