
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 xaxis and subtracting areas below the xaxis. 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 xaxis and the other is below the xaxis. 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 xaxis). 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 xaxis 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 xaxis so its signed area is negative The region from x= 6 to x= 14 is a semicircle with radius 5 above the xaxis. The region from x= 14 to x= 20 is again below the xaxis 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 xaxis) of the regions between x= a and x= b. 

Tags 
find, graph, integrals, values 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
$k2^x+2^x=8$, find the possible values of $k$  jiasyuen  Algebra  1  July 8th, 2015 05:13 AM 
Find All Values  HellBunny  Algebra  26  May 2nd, 2012 09:40 AM 
find values of ? that correspond to the ? values?  space55  Calculus  0  October 10th, 2010 03:23 PM 
Values of the derivative greatest and least graph  wicked357  Calculus  3  January 25th, 2010 01:02 PM 
Values of X being discontinuous graph.  wicked357  Calculus  1  January 24th, 2010 09:59 AM 