Ask questions and get helpful responses.

Calc 2

Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (5, 125), and the x-axis.

its not 625/3

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. the tangent has slope y' = 10x
    so at (5,125) the tangent line is
    y-125 = 50(x-5)
    y = 50x - 125
    The boundary changes where the line intersects the x-axis, so the area is thus seen to be
    ∫[0,5/2] 5x^2 dx + ∫[5/2,5] (5x^2 - (50x-125)) dx = 625/24 + 625/24 = 625/12

    or, using horizontal strips of width dy,
    ∫[0,125] ((y+125)/50 - √(y/5)) dy = 625/12

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    👤
    oobleck

Respond to this Question

First Name

Your Response

Still need help? You can ask a new question.