Post a New Question

Calculus II

posted by .

Find the area of the region between y = x sin x and y = x for 0 ≤ x ≤ pi/2

  • Calculus II -

    well, the first question is do they cross?

    xsinx=x
    sinx=1
    x=PI/2
    so no crossing.

    Then area is

    int (x-xsinx)dx over limits.

    x^2/2 -sinx+xcosx

    PI/2)^2/2-1 check that.

  • Calculus II -

    I so happens that the two functions intersect at
    x = 0 and x = π/2, the domain of our area

    area
    = [integral] (xsinx - x)dx from 0 to π/2
    = sinx - xcosx - (1/2)x^2 | from 0 to π/2
    = sinπ/2 - π/2(cosπ/2) - π^2/8 - (sin0 - 0 - 0)
    = 1 - 0 - π^2/8
    = 1 - π^2/8
    = - .2337

    OOPS, just realized that my assumption that the trig curve was above the straight line was false, so we have to reverse the integrand

    area = integral (x - xsinx)dx

    make the necessary changes, only the signs will be affected, or
    we could just take the absolute value of each of my lines.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc II

    Find the area of the region between y = x sin x and y = x for 0 ≤ x ≤ pi divided by 2
  2. Calculus 3

    Compute the average value of following fuction over the region R?
  3. math

    Find the area of the region between the curves y = sin x and y = x^2 - x, 0 ≤ x ≤ 2.
  4. algebra 1 help please

    4) a student score is 83 and 91 on her first two quizzes. write and solve a compound inequality to find possible values for a thord quiz score that would give anverage between 85 and 90. a. 85≤83+91+n/3 ≤90; 81≤n≤96 …
  5. 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
  6. PRE - CALCULUS

    Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π A. x2 - y2 = 6; -6 ≤ x ≤ 6 B. x2 - y2 = 36; -6 ≤ …
  7. math

    Find the area of the region. (Round your answer to three decimal places.) between y = cos t and y = sin t for −π/2 ≤ t ≤ π/2
  8. Calculus III

    Evaluate ∭W f(x,y,z)dV for the function f and region W specified: f(x,y,z) = 18(x+y) W: y≤ z≤x ; 0≤y≤x ; 0≤x≤1 ∭W (18(x+y))dV =
  9. Differentials (calc)

    Solve the Poisson equation ∇^2u = sin(πx) for 0 ≤ x ≤ 1and 0 ≤ y ≤ 1 with boundary conditions u(x, 0) = x for 0 ≤ x ≤ 1/2, u(x, 0) = 1 − x for 1/2 ≤ x ≤ 1 and 0 everywhere …
  10. Calculus

    Use the limit process to find the area of the region between the graph of the function and the y-axis over the given y-interval. f(y) = 7y, 0 ≤ y ≤ 2

More Similar Questions

Post a New Question