Posted by Melanie on Friday, August 15, 2008 at 6:23am.
What is the area of the region bounded by y=x^2, the tangent to this parabola at (1, 1) and the xaxis?
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  Reiny, Friday, August 15, 2008 at 9:47am
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 = 2x1, which would result in an xintercept 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 xaxis, y=2x1 and x=1
let me know if you got 1/12.
Answer This Question
Related Questions
 calculus 2  Find the area of the region bounded by the parabola y = 5x^2, the ...
 calculus 2  Find the area of the region bounded by the parabola y = 3x^2, the ...
 calculous  Find the area of the region bounded by the parabola y = 4x^2, the ...
 calculous  Find the area of the region bounded by the parabola y = 4x^2, the ...
 calculus  Find the area of the region bounded by the parabola y=x^2 , the ...
 Parabola Ques  Find the point P on the parabola y^2 = 4ax such that area ...
 Calc.  Find the area of the region bounded by the parabola y=x^2, the tangent ...
 Calculus  Sketch a graph of the parabola y=x^2+3. On the same graph, plot the ...
 Applications of definite integrals  find the area of the region bounded by the ...
 math  1) A region is bounded by the line y = x and the parabola y = x2  6x + ...
More Related Questions