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 April 11th, 2017, 07:05 PM #1 Member   Joined: Feb 2017 From: henderson Posts: 36 Thanks: 0 Use the following graph to find the values of the integrals. Enter the exact answers.    Help guys! I do not know what to do! My tutor told me to use rectangle, triangle and circle formulas! HOW? April 12th, 2017, 02:01 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,939 Thanks: 2210 Each integral can be evaluated as a combination of areas, adding areas above the x-axis and subtracting areas below the x-axis. That's not a full specification, but you should have been taught this method. The first integral corresponds to a square (of side length 2) and two congruent triangles that "cancel" (as one is above the x-axis and the other is below the x-axis. Hence its value is 4. The second integral corresponds to half of a circle with radius 4. Hence its value is 8$\pi$ (as the entire area is above the x-axis). Is that sufficient help? April 12th, 2017, 04:50 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 From x= 0 to x= 2, the region under the graph (down to y= 0) is a 1 by 1 rectangle. I From x= 2 to 3 the region under the graph is a triangle with base 1 height 2. Now the graph goes below the x-axis so will have negative "signed area". The region from 3 to 4 above the graph (up to y= 0) is a triangle with base 1 and height 2. The region from 4 to 6 is a triangle with height and base 2 but is still below the x-axis so its signed area is negative The region from x= 6 to x= 14 is a semi-circle with radius 5 above the x-axis. The region from x= 14 to x= 20 is again below the x-axis and is a trapezoid with bases of length 6 and 3 and height 4. The integral "from a to b" is the sum of the areas (including the negatives for regions below the x-axis) of the regions between x= a and x= b. Tags find, graph, integrals, values 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 jiasyuen Algebra 1 July 8th, 2015 05:13 AM HellBunny Algebra 26 May 2nd, 2012 09:40 AM space55 Calculus 0 October 10th, 2010 03:23 PM wicked357 Calculus 3 January 25th, 2010 01:02 PM wicked357 Calculus 1 January 24th, 2010 09:59 AM

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