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. 👍 0
  2. 👎 0
  3. 👁 314
  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. 👍 0
    2. 👎 0

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

    Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

  3. 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

  4. Calculus

    Find the number a such that the line x = a divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.

  1. 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

  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,

  3. 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 = 0, x = 0, x = 3, about the y-axis

  4. 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

  1. Math

    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 = −x^2 + 14x − 45, y = 0; about the x-axis

  2. Calculus 2

    use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y=x^(1/3), y=0, x=1

  3. 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

  4. Cal

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^2, y=0, x=4, x=5; about y=−2

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