calculus

posted by .

Sketch the region in the first quadrant enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=10cosx, y=10sin2x,x=0

  • calculus -

    first solve the two to find where they cross
    10sin2x = 10cosx
    sin2x - cosx = 0
    2sinxcox - cosx = 0
    cosx(2sinx - 1) = 0
    cosx = 0 or sinx = 1/2
    x = π/2 or x = π/4 in the first quadrant

    so I would do it in two integrals
    1. integral [ 10sin2x] from 0 to π/4
    2. integral [10cosx] from π/4 to π/2

    Area = -20cos2x | from 0 to π/4 + 10sinx | from π/4 to π/2
    = (-20cos2(π/4) + 20cos 0) + (10sinπ/2 - (10sinπ/4))
    = 0 + 20 + 0 - 10/√2
    = 20 - 10/√2
    = (20√2 - 10)/√2 = appr. 12.929

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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=3sqrt(x) , y=3 and 2y+3x=6.
  2. 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=5 rootx, y=5, and 2y+2x=7.
  3. 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=3sqrtx and y=3 and 2y+2x=5
  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=3sqrtx , y=3 , 2y+2x=5
  5. 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
  6. 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. x+y^2=42, x+y=0
  7. 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 sqrt x,y=3 and 2y+1x=4
  8. Calculus 2

    Sketch the region in the first quadrant enclosed by y=7/x, y=2x, and y=x/2. Decide whether to integrate with respect to x or y. Then find the area of the region.
  9. 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 = 4√x and y = 5 and 2y+2x = 6.
  10. 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. y = 5x^2 and y = x^2+6

More Similar Questions