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November 22nd, 2014, 07:58 AM   #1
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Intersection of a trig funct and polynomial

This is problem #19, section 5.1 on Stewart's 7th edition Calculus.

Is asks to sketch the region enclosed by given curves and find it's area


$\displaystyle \begin{align*} y&=cos\pi x \end{align*}$ , $\displaystyle \begin{align*} y&=4x^2-1 \end{align*}$

The integration and finding the area are easy. So is sketching the graphs (that's how i found the intersection points x=+- 1/2). But i'm having trouble solving the equation

$\displaystyle \begin{align*} cos\pi x&=4x^2-1 \end{align*}$ to find the intersection points mathematically. Any suggestions on how to solve this besides Newton's method?

Last edited by fsswim11; November 22nd, 2014 at 08:09 AM.
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November 22nd, 2014, 08:30 AM   #2
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by observation, they both have x-intercepts at x = 1/2 ... if the functions were different, you'd need an approximation method.
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