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The area bounded by the curves $y^2$ = 9x, x - y + 2 = 0 is given by
a) 1

b) 1/2

C) 3/2

d) 5/4
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What is the final answer. Is it b)??
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Answer is 1/2
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2 Answers

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In the following problem first, we have a parabola ($y^{2}= 4ax$) and the equation of a straight line given by ($y = mx + c$). We see the graph comes like this.

So , now let us equate the 2 equations:

$x + 2 = 3\sqrt{x}$

$(x + 2) ^{^{2}}= 9x$

$x^{^{2}} - 5x + 4 = 0$

By simplifying this quadratic equation we get $x = 4$ and $x = 1$ .

Similarly, substitute the values of x in the equation, we get $y = 6$  and $y = 3$.

Now by using Integration, we solve the problem

Area bounded by 2 curves is given by area bounded by the parabola - Area bounded by the St Line 

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When d two equations are solved then the following values of y are obtained:

At y=6, x=4.

And for y=3, x=1. The area under d curve therefore varies accordingly.
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