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November 22nd, 2014, 07:58 AM  #1 
Newbie Joined: Oct 2014 From: los angeles Posts: 6 Thanks: 0  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 $\displaystyle \begin{align*} y&=cos\pi x \end{align*}$ , $\displaystyle \begin{align*} y&=4x^21 \end{align*}$ 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 $\displaystyle \begin{align*} cos\pi x&=4x^21 \end{align*}$ 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. 
November 22nd, 2014, 08:30 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,034 Thanks: 1621 
by observation, they both have xintercepts at x = 1/2 ... if the functions were different, you'd need an approximation method.


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