My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
April 11th, 2017, 07:05 PM   #1
Joined: Feb 2017
From: henderson

Posts: 36
Thanks: 0

Unhappy 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!
Bobbyjoe is offline  
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?
skipjack is offline  
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.
Country Boy is offline  

  My Math Forum > College Math Forum > Calculus

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

Copyright © 2019 My Math Forum. All rights reserved.