# Thread: How did they simplify this?

1. ## How did they simplify this?

This: $2\pi\int_1^4 \sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

To get: $\pi\int_1^4\sqrt{4y+1}dy$

I thought they found the common denominator under the radical, distributed the $\sqrt{y}$, then divided by 2. Apparently I'm wrong unless I did the algebra incorrectly.

2. Originally Posted by c_323_h
This: $2\pi\int_1^4 \sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

To get: $\pi\int_1^4\sqrt{4y+1}dy$

I thought they found the common denominator under the radical, distributed the $\sqrt{y}$, then divided by 2. Apparently I'm wrong unless I did the algebra incorrectly.
It's simpler to bring the 2 inside the square root:

$2\pi\int_1^4 \sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 2\sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 \sqrt{4y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 \sqrt{4y+1}dy$

-Dan

3. Originally Posted by topsquark
It's simpler to bring the 2 inside the square root:

$2\pi\int_1^4 \sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 2\sqrt{y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 \sqrt{4y}\sqrt{1+\frac{1}{4y}}dy$

$\pi\int_1^4 \sqrt{4y+1}dy$

-Dan
ugh...why do they keep doing this to me? math beats me up sometimes jk, Thanks!

4. Originally Posted by c_323_h
ugh...why do they keep doing this to me? math beats me up sometimes jk, Thanks!
Don't worry about it. It happens to the best of us.

-Dan