calculus

1. Let R be the region in the first quadrant enclosed by the graphs of y=4-X , y=3x , and the y-axis.
a. Find the area of region R.
b. Find the volume of the solid formed by revolving the region R about the x-axis.

  1. 👍
  2. 👎
  3. 👁
  1. need the intersection ....
    3x = 4-x
    4x=4
    x = 1
    height of revolved region = radius of rotation
    = 4-x - 3x = 4 - 4x

    area = ∫(4-4x) dx from 0 to 1
    = [4x - 2x^2] from 0 to 1
    = (4 - 2) - 0
    = 2

    volume = π∫ (4-4x) dx from 0 to 1
    = π∫(16 - 32x + 16x^2) dx from 0 to 1
    = π[16x - 16x^2 + (16/3)x^3 ] from 0 to 1
    = π( 16 - 16 + 16/3 - 0)
    = 16π/3

    check my arithmetic

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Let R be the region in the first quadrant enclosed by the graph of f(x) = sqrt cosx, the graph of g(x) = e^x, and the vertical line pi/2, as shown in the figure above. (a) Write. but do not evaluate, an integral expression that

  2. Calculus

    Let R be the region enclosed by the graphs y=e^x, y=x^3, and the y axis. A.) find R B.) find the volume of the solid with base on region R and cross section perpendicular to the x axis. The cross sections are triangles with height

  3. calculus

    R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

  4. math (9)

    Find the area of the region enclosed by these graphs and the vertical lines x = 0 and x = 3 f(x)=-x^2+2x+4 g(x)=-x+4

  1. Calculus AB...I really need help

    The region in the first quadrant enclosed by the coordinates axes, the line x=pi, and the curve y= cos(cosx) is rotated about the x-axis. What is the volume of the solid generated.

  2. Calculus

    The shaded regions R1 and R2, shown below, are enclosed by the graphs of f(x)= −x^2 and g(x)= −2^x. (gyazo.com/7bcf02392ff69e2a1280588308342e8e) Find the x- and y-coordinates of the three points of intersection of the graphs

  3. math (8)

    Find the area of the region enclosed by these graphs and the vertical lines x = 3 and x = 5 f(x)=x^2+5 g(x)=1

  4. calculus

    Let R be the region in the first quadrant that is enclosed by the graph of y = tanx, the x-axis, and the line x = π/3 h. Find the area of R i. Find the volume of the solid formed by revolving R about the x-axis

  1. calculus

    R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.

  2. math

    In which quadrant does the terminal side of the angle with measure -245 degree lie? Quadrant I Quadrant IV Quadrant III Quadrant II None

  3. Calc AB

    What is the area of the region in the first quadrant enclosed by the graph of y=e^(x^2/4) and the line y=0.5? When I graphed the two functions they don't even connect so the answer would be infinity. What am I doing wrong>

  4. AP Calculus

    Let R be the first quadrant region enclosed by the graph of y= 2e^-x and the line x=k. a) Find the area of R in terms of k. b) Find the volume of the solid generated when R is rotated about the x-axis in terms of k. c) What is the

You can view more similar questions or ask a new question.