Please help me with this problem. I have been trying 2 do it 4 half an hour and still can figure out. Thank You!

Find the area of the region bounded by the hyperbola 25x2 - 4y2 = 100 and the line x = 3.

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- Sep 9th 2009, 03:10 PMshah4u19area of the region bounded by the hyperbola?
Please help me with this problem. I have been trying 2 do it 4 half an hour and still can figure out. Thank You!

Find the area of the region bounded by the hyperbola 25x2 - 4y2 = 100 and the line x = 3. - Sep 9th 2009, 03:47 PMseld
So the area looks a little like a slice of a circle right?

the easiest way to do it is turn y in terms of x.

Since you need both the positive and negative portion instead of doing 2 integrals you can just take the integral to get the region above the x axis and multiply it's area by 2.

can you take it from there? - Sep 9th 2009, 03:55 PMshah4u19
Thanks! But do i substitute x = 5 sec d(theta), If yes then when I continue, I get stuck on the way.

- Sep 9th 2009, 04:07 PMseld

Substituting when you take the integral

well what's ?

right?

what if you let u = 2x?

and right?

when you substitute that in it gets messy.

what if you let u = 2x?

Seems like you should do a trig substitution after that, though your initial idea to substitute secant isn't wrong, just needs somewhat different coefficients.