Post a New Question

Calculus

posted by .

If 0 <= k <= pi/2 and the area of the region in the first quadrant under the graph of y = 2x-sinx from 0 to k is 0.1, then k =

(a) 0.444
(b) 0.623
(c) 0.883
(d) 1.062
(e) 1.571

  • Calculus -

    a = ∫[0,k] 2x-sinx dx
    = x^2+cosx [0,k]
    = (k^2+cos(k))-(1)
    = cos(k) + k^2-1

    so, cos(k) + k^2-1 = 0.1
    k must be small, so cos(k)-1 is near 0.

    In fact, since cos(k) = 1 - k^2/2 + k^4/4! - ...

    a =~ k^2/2
    so, k =~ √0.2 = 0.44

    so, (a)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I am doing the AP calculus review, these are the questions I have no Idea on how to do: 1. if 0<= k <=pi/2 and the area under the curve y-cosx from x=k to x=pi/2 is 0.2, then k= 2. let F(x) be an antiderivative of (ln x)^4/x …
  2. calculus

    Find the area of the region in the first quadrant enclosed by the coordinate axes and graph of x^3+y^3=1.
  3. Calculus

    Let R be the region in the first quadrant under the graph of y=1/sqrt(x) for 4</=x</=9. (a)Find the area of R. I took the antideriative. Then, I plugged in the 9 and 4. I got 2. (b) If the line x=k divides the region R into two …
  4. calculus

    Let A be the area if the region in the first quadrant under the graph of y = cos(x) and above the line y = k for 0 < k < 1. a. Determine A in terms of k. b. Determine the value of A when k = 1/2 c. If the line y = k is moving …
  5. calculus

    can not figure out problem. (the area of the region in the first quadrant between the graph of y=x sqrt (4-x^2) and the axis is ?
  6. calculus

    given the graph of f(x) = x sinx, 0<=x<=2pi assuming that a quantity y changes at a rate of y' = xsinx, find by how much it will increase or decrease over 3pi/2 <= x <= 2pi the area under the graph from 0 to pi/2 is 1 the …
  7. calculus

    find the area enclosed by y=x^2 and y=sinx in the first quadrant.
  8. calculus

    2. Sketch the region in the first quadrant that is bounded by the graphs of y=x^3, y=4X , and 2x+y-3=0 that lies below both straight lines. Find the area of this region. I can see the graph in front of me. which function do I subtract …
  9. Calculus

    Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. Let R be the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line tangent …
  10. Calculus

    Let R be the first quadrant region enclosed by y=e^2, y=e^x and the y-axis. The area of region R is?

More Similar Questions

Post a New Question