Finding X-intercept using Intermediate Value Theorem

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Homework Statement



a.Prove that the function f(x)=x-(arctan x)^2+8arctan x -19 has one x- intercept.
b.Let Xo be the x-intercept of f(x). Use the intermediate value Theorem to find two consecutive integers n1,n2 such that n1 biger than Xo and Xo biger than n2

Homework Equations





The Attempt at a Solution

 
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dude, no one will help you unless you show some work. What forumlas you know of and were you are stuck and so on.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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