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 May 16th, 2017, 09:46 AM #1 Member   Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0 Integrals help! Ok, so I got stuck here. Find the area bounded by the x axis and the graph of the function f(x) = x^3cos(x^2) and also consists the point (1, 1/10). The last part with the point confused me, any help?  May 16th, 2017, 10:04 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 I'm going to guess that point just means they want you to integrate the bit of that graph above the x-axis, i.e. $x \in \left[0, \sqrt{\dfrac \pi 2}\right]$ Thanks from greg1313 May 17th, 2017, 02:57 AM   #3
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 Originally Posted by romsek I'm going to guess that point just means they want you to integrate the bit of that graph above the x-axis, i.e. $x \in \left[0, \sqrt{\dfrac \pi 2}\right]$
I still don't get it. How did you get 0, sqrt(pi/2)? May 17th, 2017, 03:15 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The given function, crosses the x-axis many times so has some pieces above the x-axis, others below. romsek is suggesting that you take the first of those above the x-axis. when x= 0, of course, and next, when which happens are . (By the way, "consists", here, is the wrong word. You probably mean "contains (1, 1/10)".) Thanks from sarajoveska May 17th, 2017, 03:19 AM #5 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 $x^3 \cdot \cos(x^2) =0$ at $x=0$ and whenever $x^2$ equals an odd-integer multiple of $\dfrac{\pi}{2}$ FYI, $0 < \dfrac{1}{10} < \sqrt{\dfrac{\pi}{2}}$, and $x^3 \cdot \cos(x^2) > 0$ on that same interval. $\displaystyle A = \int_0^{\sqrt{\pi/2}} x^3 \cdot \cos(x^2) \, dx$ Let $t=x^2 \implies dt = 2x \, dx$ ... $\displaystyle A = \dfrac{1}{2} \int_0^{\pi/2} t \cdot \cos(t) \, dt$ Looks like integration by parts from this point ... I'll let you finish. Thanks from greg1313 and sarajoveska Tags integrals Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post The_Ys_Guy Calculus 4 July 8th, 2016 04:35 AM joshbeldon Calculus 5 January 16th, 2015 06:41 AM Dacu Calculus 3 June 28th, 2014 04:56 AM Calii Calculus 0 November 6th, 2010 02:26 PM hector manuel Real Analysis 0 May 4th, 2009 11:16 PM

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