       Newbie question on FindRoot and NIntergrate

• To: mathgroup at smc.vnet.net
• Subject: [mg80437] Newbie question on FindRoot and NIntergrate
• From: "Hoa Bui" <hoabui05 at gmail.com>
• Date: Wed, 22 Aug 2007 04:49:45 -0400 (EDT)

```Dear all,

I have a series of points:
In:=points
Out={{0.0001,0.359381},{0.0002866,0.403984},{0.000821394,0.454122},{0.00235411,0.510482},{0.00674688,0.573838},{0.0193365,0.645056}}

Define one of my function as the trapezoidal area created by these
points up to some x:
linNx = Interpolation[points, InterpolationOrder -> 1];
ff[x_] := Integrate[linNx[s], {s, 0.0001, x}]

Define the second function as a power law:
gg[x_] := 0.9 x^(1/0.9)

My third function is the root of the equation:
hh[x_] := FindRoot[ff[y] == gg[x], {y, 0.0001, 0.019}];

I can evaluate h at specific values of x, e.g. h[0.001] ({y ->
0.00107654}), h[0.01] ({y -> 0.0101302}), etc...

Now say I want to use hh[x] in an integral,
NIntergrate[hh[x],{x, 0.0001, 0.019}]
obviously it doesn't work, and I have tried using Solve instead of
FindRoot but it also did not output a numerical value for the integral
because the inverse function is not in closed form or something..

Is there a way for me to compute the integral of hh[x] ?

Thank you all so much,
Hoa Bui

```

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