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    A parametric equation "C" is given by x=3t^2 and y=2t^3

    A tangent having an equation of y= 2x-8 is drawn to C at P where t =2.The tangent meets the curve again at the point Q(3,-2).

    Find the area of the region bound by the arcs OP , and OQ of the curve C and the line PQ.

    Here's the diagram of the equation.
    http://www.wolframalpha.com/input/?i...chronous=false

    This is a C3 question and even my sir couldn't do it!Help needed!

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    This question was posted previously on TSR and no one could solve it
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    (Original post by Doink-the-Clown)
    A parametric equation "C" is given by x=3t^2 and y=2t^3

    A tangent having an equation of y= 2x-8 is drawn to C at P where t =2.The tangent meets the curve again at the point Q(3,-2).

    Find the area of the region bound by the arcs OP , and OQ of the curve C and the line PQ.

    Here's the diagram of the equation.
    http://www.wolframalpha.com/input/?i...chronous=false

    This is a C3 question and even my sir couldn't do it!Help needed!

    Spoiler:
    Show
    This question was posted previously on TSR and no one could solve it
    AT Q t=-1 and at the Q' - which is the mirroring of Q on the x - t=1
    at t=1 x=3 , and the line meets the x at x=4
    So you should to calculate more integral.
    1. The area between the C and axis x from O to Q' that is from t=0 to t=1 and you should to double it.
    2. Similarly calculate the area bellow the C between t=1 (x=3) and t=2 (x=12)
    that is between Q'P
    3. substract the area of triangle with sides of 12-4=8 and 16
    4. Add the area of trangle with sides of 4-3=1 and |-2|=2
    For 1.
    \displaystyle \int^1_0 2t^3 d(3t^2)= \int^1_0 2t^3\cdot 6t\ dt= \int^1_0 12t^4\ dt
    and multiply by 2 or integrate from t=-1 to t=1
 
 
 
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