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please help me out with the question below thanks.
find the area of the region bounded by the hyperbola
9x^2 - 4y^2 = 36
and the line x = 3
Let's substitute y=0 into the hyperbola equation, this will give us the point of intersect
of the hyperbola with x-axis :
9*x²-0=36
x²=4
x=±2
Now, let's write the hyperbola in different form :
9x²-4y²=36 -> 4y²=9x²-36 -> 2y=√9√(x²-4) -> y=⅔√(x²-4).
Now, the area will be from x=2 to x=3 . Therefore :
3
A=∫⅔√(x²-4) dx .
2
I will leave the rest of the calculation for you as an exercise .
Alon.
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Answers by Expert:
Alon Mandes
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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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M.A in Mathematics & Bs.c in Electronics.
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