My Math Forum Use the following graph to find the values of the integrals.

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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: 20,622 Thanks: 2075 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.

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