Math integrals

posted by .

What is the area of the region bounded by y=x^2, the tangent to this parabola at (1, 1) and the x-axis?
Since it says that the parabola passes through 1,1 can I assume that the line is y = x or is that completely wrong?

Doing that I got ∫ x - x^2 dx (where the interval from a to b goes from 0 to 1)
so the solved integral would be
x^2/2 - x^3/3] 0 to 1
= [(1)^2/2 - (1)3/3] - 0
= 1/2 - 1/3
= 1/6

What should I have done if it's wrong?

  • Math integrals -

    The tangent line is not y = x
    Since the derivative of y = x^2 is dy/dx = 2x, at (1,1) dy/dx = 2, so the tangent line has a slope of 2

    its equation would be y = 2x + b, with (1,1) on it
    So, 1 = 2(1) + b, ------> b = -1

    the tangent equation is y = 2x-1, which would result in an x-intercept of (1/2,0).

    I would take the area between y = x^2 from 0 to 1 minus the right -angled triangle formed by the x-axis, y=2x-1 and x=1

    let me know if you got 1/12.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc.

    Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, …
  2. math

    1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis?
  3. calculus

    Find the area of the region bounded by the parabola y=x^2 , the tangent line to this parabola at (10, 100), and the x-axis.
  4. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.
  5. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.
  6. Calculus

    Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) …
  7. Applications of definite integrals

    find the area of the region bounded by the parabola y^2= 16x and its latus rectum
  8. Parabola Ques

    Find the point P on the parabola y^2 = 4ax such that area bounded by parabola, the X-axis and the tangent at P is equal to that of bounded by the parabola, the X-axis and the normal at P.
  9. calculus 2

    Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.
  10. calculus 2

    Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

More Similar Questions