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Let f(x) = 4x^(3) + 1. If the area of the region bounded by f(x) and x-axis from x = 0 to x = a is same as the area of region bounded by f(x) and x-axis from x = a to x = 3 then a lies in (a > 0) |
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Answer» (0,1) `int_(O)^(a) f(x) DX = int_(a)^(3) f(x) dx` `implies a^(4) + a = 84 - (a^(4) + a)` `a^(4) + a - 42 = 0` Let `g(a) = a^(4) + a - 42` `g(0) < 0, g(1) < 0, g(3) > 0` By IVT `a in (2, 3)`. |
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