What do I input to find the area of the region bounded by the hyperbola?

I am trying replicate the problem below in Matlab. What is the input I use?

Thanks!

Answer 1

[Prakhar Rai]

By using definite integral over the intersection points of the two functions.

Area b/w two curves = Integral (f(x)-g(x)) ;

[Rachel Bowlin]

What am I doing wrong?

[Prakhar Rai]

Create the function f(x)= 3/2 sqrt(x^2-4),f(x)= - 3/2 sqrt(x^2-4)

The area b/w the functions would be Integral(f(x) from x [2:3]) + Integral(-f(x) from x [2:3]) as at x=2 hyperbola becomes 0 and x=3 the two functions cross.

Due to symmetry:

Integral(f(x) from x [2:3]) =Integral(-f(x) from x [2:3])

So just calculate Integral(f(x) from x [2:3]) and multiply by 2.

Twice since area is same both above and below x axis.

fun = @(x) 3./2 .* sqrt((x.^2)-4);

ans = 2 .* integral(fun,2,3);

You need to pass function handle in integral().

Also as mentioned in errors use '.^' and '.* ' instead of ^ and * .

Please go through this page: Integration to get complete understanding.

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