1.

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)

Answer»

(0,1)
`(1, 3/2)`
`(3/2 , 2)`
`(2, 3)`

Solution :
`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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