calculus

Sketch the region bounded by the curves y = x^2, y = x^4.
1) Find the area of the region enclosed by the two curves;
2) Find the volume of the solid obtained by rotating the above region about the x-axis;
3) Find the volume of the solid obtained by rotating the above region about the horizontal line with
equation y = 1 .

  1. 👍 0
  2. 👎 0
  3. 👁 383
  1. The region bounded by the two curves is between x = -1 and x = +1. Plot the two curves and you will see why.

    1) Integrate (x^2 - x^4)dx from x = -1 to x = 1

    2) Integrate pi*y1^2 - pi*y2^2 dx
    = pi*(x^4 - x^8)dx from x = -1 to x = 1.
    y1(x) = x^2
    y2(x) = x^4

    3) Integrate pi[(1 - y2)^2 - (1 - y1)^2]
    dx from -1 to +1

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. CALCULUS

    Sketch the region enclosed by the given curves. y = 4/X y = 16x, y = 1X/16 x > 0 and the area between the curves

    asked by LAUERN PLEASE HELP on April 12, 2014
  2. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

    asked by Danni on March 22, 2017
  3. CALCULUS

    Sketch the region enclosed by the given curves. y = tan 3x, y = 2 sin 3x, −π/9 ≤ x ≤ π/9 then then find the area. i can sketch but cant find correct area

    asked by LAUERN PLEASE HELP on April 12, 2014
  4. calculus

    1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Use the method of cylindrical shells to find the volume V

    asked by Anonymous on January 30, 2020
  1. calculus

    Consider the curves y = x^2and y = mx, where m is some positive constant. No matter what positive constant m is, the two curves enclose a region in the first quadrant.Without using a calculator, find the positive constant m such

    asked by John on March 4, 2012
  2. Calculus

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,y=1; about y=7

    asked by Anonymous on April 18, 2017
  3. math

    Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =1/4x, x > 0 Find the area.

    asked by LC on August 29, 2017
  4. Calculus

    Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3(x^(1/2)) , y=5 and 2y+3x=6

    asked by Kathy on October 26, 2012
  1. Calculus

    Find the area of the region bounded by the curves y = sin x, y = csc^2x, x = pi/4, and x = (3pi)/4.

    asked by Slaya on March 13, 2020
  2. calculus 2

    Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y

    asked by TayB on January 22, 2016
  3. Calculus

    Sketch the given region R and then find its area. R is the region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

    asked by Anna Kirakosyan on November 3, 2016
  4. calculus

    find the centroid of the plane region bounded by the curves y = cos x, y=sinx, x=0,

    asked by zoe on October 31, 2011

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