12th Class Mathematics Application of integrals

  • question_answer 10) Find the ara bounded by the curve x2 = 4y and the line x = 4y – 2.  

    Answer:

    Given curves are             x2 = 4y                          ?. (1)             x = 4y ? 2                     ?..(2)               For (1), x2 = 4y             (1)   and (2)  (4y ? 2)2 = 4y  16y2 + 4 ? 16y = 4y 16y2 ? 20y + 4 = 0 4y2 ? 5y + 1 = 0 4y2 ? 4y ? y + 1 = 0 4y (y ? 1) ? (y ? 1) = 0              y = 1, ¼             x = 2, ? 1          [by (2)]    Points of intersection are (?1, ) and (2, 1)                                        

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