math, calculus

1. Consider the region bounded by the curves y=|x^2+x-12|, x=-5, and x=5 and the x-axis.

A. Set up a sum of integrals, not containing an absolute value symbol, that can be used to find the area of this region.

B. Find the area of the region by using your answer from part A. Don’t approximate with your calculator.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. Since y < 0 for -4 < x < 3,

    ∫[-4,-4] y dx + ∫[-4,3] -y dx + ∫[3,5] y dx

    Now just plug in the polynomial for y, and evaluate each integral.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 7y^2, y ≥ 0, x = 7; about y = 2

  2. calculus

    The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 7x − 12, y = 0; about the x-axis

  3. calculus

    Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find the volume when A is revolved around the x-axis

  4. Calculus

    1. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = x, y = 0, y = 5, x = 6 2. Use the method of cylindrical shells to find the volume V generated by

  1. Calculus 2

    The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y2 − x2 = 4, y = 3; about the x-axis

  2. Calculus

    The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = (y − 7)^2, x = 16; about y = 3

  3. calculus

    1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves

  4. AP calc

    Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 8x − x^2, y = 12; about x = 2

  1. Cal 2

    Find the volume of the solid whose base is the region bounded by the x-axis, the curves y=x, y=3x^2, x=0, and x=.333333 and which has the property that each cross section perpendicular to the x-axis is an equilateral triangle.

  2. 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

  3. calc

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y=cos(7x) , x=π/14, x=0 about the axis y=−8

  4. 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,

View more similar questions or ask a new question.