calculus

Consider the following shaded region.

Find the area S of this region if a = 6, b = 3. (Give an exact answer.)
The two graphs intercept at 0 and the other limit is not given. The integral is int(ax-x^2)-(bx. So y=ax+x^2 is the graph on top and y=bx is at the bottom.

  1. 0
  2. 0
  3. 104
asked by aimee
  1. The upper limit of the integration will be where the curves intersect.

    That is where 6x - x^2 = 3x.

    x^2 -3x = x(x-3) = 0
    x = 0 or 3

    Now calculate
    int(6x-x^2)-(3x)dx from 0 to 3
    = int 3x - x^2 dx from 0 to 3
    = [3x^2/2 - x^3/3]@x=3 - 0
    (Since the value of the indefinite integral in brackets, at x = 0, is 0)
    = 27/2 - 27/3 = 27/6 = 9/2

    1. 0
    2. 0
    posted by drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A carpet company uses the template to design a rug. Write an expression for the area of the shaded region as it relates to the variable length x answer. The shaded square has a white square within it. On the outside of the shaded

    asked by Stacy on January 5, 2018
  2. math

    A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

    asked by Anonymous on August 31, 2016
  3. statistics finding the shaded region

    Find the area of the shaded region. The graph depicts the IQ score of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The shaded region numbers are 85-120

    asked by Kelli on December 12, 2014
  4. algebra1

    graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region common to all four

    asked by jenika on May 17, 2012
  5. algebra1

    graph the system of inequalities, and classify the figure created bu the solution region. y¡Ü4x+4 y¡Ü-0.25x+4 y¡Ý4x-1 y¡Ý-0.25x-1 a)the shaded region is a plane minus a rectangle b)there is no region common to all four

    asked by jenika on May 17, 2012
  6. Math

    A man owns a rectangular piece of land. The land is divided into four rectangular pieces, known as Region A, Region B, Region C, and Region D. One day his daughter, Nancy, asked him, what is the area of our land? The father

    asked by Josh on May 8, 2014
  7. math- geometry

    I will try and explain this since I can't draw the picture that went with this question. A circular glass overlay was placed on the top of a circular table. Find the area of the shaded region, rounding to the nearest tenth. The

    asked by sara on May 6, 2016
  8. Calculus

    Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. Let R be the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line

    asked by Jessy152 on February 27, 2013
  9. algebra

    directions Write a system of inequalities for the shaded region described. The shaded region is a rectangle with vertices at (2,1)(2,4)(6,4)

    asked by kim on March 31, 2013
  10. Math

    Marian drew a picture of two circles.She wanted to shade only the outer circle. WHich of the following is closest to the area of the shaded region? The shaded region of the outer circle's radius is 5 and the inside circl'es radius

    asked by Jerald on April 18, 2013

More Similar Questions