math

posted by .

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 -

    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, …
  2. Calculus

    You are given the four points in the plane A=(7,4) ,B=(9,-3) ,C=(13,5) , and D=(16,-2 . The graph of the function consists of the three line segmentsAB ,BC and CD . Find the integral between x= 16 and x= 7 by interpreting the integral …
  3. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value …
  4. math/calculus

    You are given the four points in the plane A(-3,6),B(0,-6),C(5,7),D(8/-7) . The graph of the function f(x) consists of the three line segments AB ,BC and CD . Find the integral f(x)from -3 to by interpreting the integral in terms of …
  5. math/calculus

    You are given the four points in the plane A(-3,6),B(0,-6),C(5,7),D(8/-7) . The graph of the function f(x) consists of the three line segments AB ,BC and CD . Find the integral f(x)from -3 to by interpreting the integral in terms of …
  6. Math: Calculus

    You are given the four points in the plane A = (5,-6), B = (9,1), C = (14,-6), and D = (19,2). The graph of the function f(x) consists of the three line segments AB, BC and CD. Find the integral f(x)dx from 5 to 19 by interpreting …
  7. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the …
  8. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the …
  9. math

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the …
  10. calculus

    You are given the four points in the plane A = (-3,7), B = (-1,-6), C = (4,6), and D = (6,-1). The graph of the function f(x) consists of the three line segments AB, BC and CD. Find the integral interval -3 to 6 f(x)dx by interpreting …

More Similar Questions