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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $ P_1 : y = 4x^2 $ and $ P_2 : y = x^2 + 27 $ be two parabolas. If the area of the bounded region enclosed between $ P_1 $ and $ P_2 $ is six times the area of the bounded region enclosed between the line $ y = ax,; a > 0 $ and $ P_1 $, then $ a $ is equal to:
Solution
Area bounded between $ P_1 $ & $ P_2 $ is
$ \int_{-3}^{3} ((x^2 + 27) - 4x^2),dx $
$ = 2 \int_0^3 (27 - 3x^2),dx = 2[27x - x^3]_0^3 $
$ = 2(81 - 27) = 108 $
$\therefore$ Area between $ P_1 $ & $ L $ is $ 18 $ sq. units
[Image used in solution — second graph]
Area between $ x^2 = 4ay $ and $ x = ay $ is
$ \frac{8a^2}{3m^3} $
$ \therefore \frac{(1/16)^2}{3(1/\alpha)^3} = 18 $
$ \Rightarrow \frac{8}{16 \cdot 16} \cdot \frac{\alpha^3}{3} = 18 $
$ \Rightarrow \alpha = 12 $
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