Calculus

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

  1. 👍 0
  2. 👎 0
  3. 👁 346
  1. A quick peek at our problem:
    https://www.wolframalpha.com/input/?i=plot+y+%3D+sin+x%2C+y+%3D+csc%5E2x

    looks like they intersect at x = π/2 and there is symmetry
    so we can take
    area = 2∫ (csc^2 x - sinx) dx from π/4 to π/2
    recalling that the derivative of cotx = -sec^2 x

    = 2[ (- cotx + cosx) ] from π/4 to π/2
    = 2 ( (-cot π/2 + cos π/2 - (-cot π/4 + cos π/4) )
    = 2( 0 + 0 - (-1 + √2/2) )
    = 2(1 - √2/2)
    = 2 - √2

    1. 👍 2
    2. 👎 0
    👨‍🏫
    Reiny
  2. Thank you!

    1. 👍 0
    2. 👎 0

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. Math

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin x, y = 8 cos x, 0 ≤ x ≤ π/4; about y = −1

  3. 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,

  4. 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.

  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

    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. 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

  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. 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.

  4. 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.)

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