calc

Find the area of the region bounded by the curves y equals the inverse sine of x divided by 4, y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

  1. 👍 0
  2. 👎 0
  3. 👁 2,276
  1. why all the words?
    y = arcsin(x/4)

    using thin horizontal strips, the area is

    a = ∫[0,π/2] (4-x) dy
    But x = 4siny, so
    a = ∫[0,π/2] (4-4siny) dy
    = 2(π-2)

    You can check your work using vertical strips:

    a = ∫[0,4] y dx
    = ∫[0,4] arcsin(x/4) dx
    = 2(π-2)

    1. 👍 1
    2. 👎 3

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. Calculus-Area between curves

    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=4*sqrt(x) , y=5 and 2y+4x=8 please help! i've been trying this problem the last couple days,

  3. Calculus

    Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area.

  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

  1. 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,

  2. Calculus

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

  3. Calculus

    1. Find the domain for the particular solution to the differential equation dy/dx=3y/x, with initial condition y(1) = 1. A. x > 0 B. x < 0 C. x ≠ 0 D. All real numbers 2. Use geometry to evaluate the integral from negative 2 to

  4. calc

    Find the centroid of the region bounded by the given curves. y = 2 sin 3x, y = 2 cos 3x, x = 0, x = π/12

  1. Calculus (Area Between Curves)

    Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859

  2. Calculus

    Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 1 into two regions with equal area. (Round your answer to two decimal places.)

  3. calculus

    Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y = 9 into two regions with equal area. (Round your answer to two decimal places.)

  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.

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