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Math Help - [SOLVED] Question on differentiation and integration?

  1. #1
    Super Member fardeen_gen's Avatar
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    [SOLVED] Question on differentiation and integration?

    Which of the following is correct?

    A) ∫ from 0 to x of A sin Bx dx = A/B(cos Bx – 1)

    B) ∫ x(a + bx) dx = x ∫(a +bx) dx + (a +bx) ∫ x dx

    C) ∫ from (r – a) to (r + a) of –(GM/2ar) dz = -GM/r

    D) d(1 + x^1/4){1 + x^(1/2)}{1 – x^(1/4)}/dx, then dy/dx = -1

    More than one options are correct. I got only D. Which others are correct?
    Last edited by fardeen_gen; June 30th 2008 at 07:53 AM.
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by fardeen_gen View Post
    Which of the following is correct?

    A) ∫ from 0 to x of A sin Bx dx = A/B(cos Bx 1)

    B) ∫ x(a + bx) dx = x ∫(a +bx) dx + (a +bx) ∫ x dx

    C) ∫ from (r a) to (r + a) of (GM/2ar) dz = -GM/r

    D) d(1 + x^1/4){1 + x^(1/2)}{1 x^(1/4)}/dx, then dy/dx = -1

    More than one options are correct. I got only D. Which others are correct?
    A & B are indeed false.

    For C :

    \int_{r-a}^{r+a} -\frac{GM}{2ar} dz=-\frac{GM}{2ar} \int_{r-a}^{r+a} dz=-\frac{GM}{2ar} \cdot [(r+a)-(r-a)]=-\frac{GM}{2ar} \cdot (2a)=-\frac{GM}{r}




    D is correct
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