# [SOLVED] Question on differentiation and integration?

• Jun 30th 2008, 06:15 AM
fardeen_gen
[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?
• Jun 30th 2008, 09:29 AM
Moo
Hello,

Quote:

Originally Posted by fardeen_gen
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 :

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

(Wink)

D is correct