I need to find the area of the region between the parabpla y^2 = 16x an the line 4x-3y=4.

I understand that i need to get them to both equal y but when i do that i seem to confuse myself and get really odd values.

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- January 26th 2011, 12:24 AMmencoArea Integral
I need to find the area of the region between the parabpla y^2 = 16x an the line 4x-3y=4.

I understand that i need to get them to both equal y but when i do that i seem to confuse myself and get really odd values. - January 26th 2011, 01:22 AMFernandoRevilla
Certainly we don't obtain rational solutions ( it appears ) but, what is the problem?

Fernando Revilla - January 26th 2011, 01:52 AMmenco
In my text book it shows that i should have the curves equal to y. So that I can find the x intercepts and work with the integral from there. However I can seem to figure out a solution for y^2=16x and 4x-3y=4. When I tried i got y=4 sqrt x and y=-(4(-x-1)/3) but i dont think thats right.

- January 26th 2011, 03:17 AMmr fantastic
If you're studying calculus you're expected to know how to solve simultaneous equations.

I suggest finding the area between x = y^2/16 and x = (4 + 3y)/4, in which case you need the y-coordinates of the intersection points of the two curves.

Equate: y^2/16 = (4 + 3y)/4. Solve for y. - January 27th 2011, 10:17 PMmenco
I got a result of 13.2111, -1.2111 for y co ordinates. Using this i integrated f(x)((4-3y)/4) - g(x) (y^2/16) using the y values on the integral. I got an overall result of 3.004 units^2.

Am i close? - January 28th 2011, 12:19 AMmr fantastic
No.

Your values of y are correct (to 4dp - but are you meant to use exact values?)

Using your values of y as the integral terminals, I don't get your answer (but since you only give a final answer, it's impossible to know whether your error is in the calculus, algebra or arithmetic). - January 28th 2011, 12:22 AMmenco
How do people put the working out as an image? If you know how they do this I will post up how I got to my answer

- January 28th 2011, 12:23 AMmr fantastic
- January 28th 2011, 12:53 AMmenco

I had another go the way i was intending to do it in the first place. and got a result of 1.742.

The last way I tried to combine the 2 fractions to make it a bit easier it looked like this

But i think i got that wrong - January 28th 2011, 01:05 AMmr fantastic
- January 28th 2011, 01:32 AMmenco
I am definatly struggling with integration. Can you suggest any good site i can learn from? I find my textbook very hard to follow

- January 28th 2011, 01:39 AMmr fantastic
- January 28th 2011, 04:08 AMmenco
Ok so i think i may have figured this out

And i get a final result of 28.80033927 - January 28th 2011, 05:37 AMmr fantastic