# Can I have some help on this integration question?Watch

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#1
Find the area under the curve (x^2 / a^2) + (y^2 / b^2) = 1 in the first quadrant, i.e. in the positive X and Y axis

I tried writing out the curve's equation with y the subject:

y^2 = b^2 - (b^2)(x^2)/a

but I don't know how I should integrate it from here. And also, how do I know what the limits would be?
0
5 years ago
#2
(Original post by fuzzybear)
Find the area under the curve (x^2 / a^2) + (y^2 / b^2) = 1 in the first quadrant, i.e. in the positive X and Y axis

I tried writing out the curve's equation with y the subject:

y^2 = b^2 - (b^2)(x^2)/a

but I don't know how I should integrate it from here. And also, how do I know what the limits would be?
You could let

which is an integral that can be done by substitution, say

This curve is actually an ellipse. You can determine the limits by finding the point where it crosses the x axis (in the first quadrant)
1
#3
(Original post by Indeterminate)
You could let

which is an integral that can be done by substitution, say

This curve is actually an ellipse. You can determine the limits by finding the point where it crosses the x axis (in the first quadrant)
Thanks man

two questions:

- I substituted that, integrated it and got: b[sinu]

do I have to change sinu back in terms of x, or can I just sub in the equivalent u limits (to the x limits)?

- also, I've tried finding the point where it crosses the x-axis, by subbing in y = 0 for:

y = b*(1 - x^2 / a)^(1/2)

so that either b = 0, or (1 - x^2 / a)^(1/2) = 0

so would x = square root of a ?
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