Question

Find the area of the shaded region in each of the following diagram:
just to double check my answer.. @ganeshie8

Answer 1

Looks you have to integrate with respect to y here

Answer 2

^yep, first get the equation solved for x in terms of y

Answer 3

\[x^2=\frac{ 10 }{ y }\]\[x=\frac{ \sqrt{10} }{ y^{-\frac{ 1 }{ 2 }} }\]\[=\sqrt{10}y^{-\frac{ 1 }{ 2 }}\]\[shaded~area=\int\limits_{2}^{10}x~dy\]\[=\sqrt{10}\int\limits_{2}^{10}y^{-\frac{ 1 }{ 2 }}~dy\]\[=\sqrt{10}[\frac{ y^{\frac{ 1 }{ 2 }} }{ \frac{ 1 }{ 2 } }]_{2}^{10}\]\[=2\sqrt{10}(\sqrt{10}-\sqrt{2})\]\[=20-2\sqrt{20}\]\[=11.06\]This is my working @ganeshie8 @agent0smith

Answer 4

It isn't y to the negative 1/2 :P

Answer 5

Other than that though it looks like you corrected your own initial mistake in step 2.

Answer 6

@agent0smith
i don't get what u mean.. xD
Can u pls show me which step i did an error ?

Answer 7

Look at step 1 and step 2, you should spot it (1/2 should not be neg)

You did it all correct otherwise, so it may have been a typo.

Answer 8

yep,it is a typo.. :)

Answer 9

Thank you @agent0smith :)

Answer 10

I thought so, given the rest :) good job.

Answer 11

yay! ^.^
Thanks again! @agent0smith