Posted by **jen** on Tuesday, January 12, 2010 at 2:32pm.

You are given the four points in the plane a=(-2,2), b=(1,-3), c=(3,6), and d=(7,-3). The graph of the function consists of the three line segments AB, BC and CD. Find the integral by interpreting the integral in terms of sums and/or differences of areas of elementary figures

- math -
**MathMate**, Tuesday, January 12, 2010 at 3:29pm
Here the integral is being evaluated, so the area of the elementary figures could be positive or negative.

It can be observed that all the line segments form a (twisted) trapezoid with the x-axis, i.e. part of the area is above the x-axis, and part of it is below.

Knowing that the area of a trapezoid is the average of the y-coordinate of the two ends, multiplied by the length, it will be possible to calculate the three areas separately.

For example, the area created by the segment AB is:

Average of y-coordinates = (2+(-3))/2=-0.5

Length = (1-(-2)) =3

Integral of segment AB=3*(-0.5) = -1.5

Repeat for the two other segments and add up the total.

## Answer This Question

## Related Questions

- Math: Calculus - You are given the four points in the plane A = (5,-6), B = (9,1...
- math/calculus - You are given the four points in the plane A(-3,6),B(0,-6),C(5,...
- math/calculus - You are given the four points in the plane A(-3,6),B(0,-6),C(5,...
- calculus - You are given the four points in the plane A = (-3,7), B = (-1,-6), C...
- Calculus - You are given the four points in the plane A=(7,4) ,B=(9,-3) ,C=(13,5...
- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- math - LEt f and g be continous functions with the following properties i. g(x...
- calculus - LEt f and g be continous functions with the following properties i. ...
- calculus - LEt f and g be continous functions with the following properties i. ...
- calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...

More Related Questions