Definite IntegrationHard
Question
One of the values of ′a′ for which the area bounded by the curve y = 8x2 - x5, straight lines x = 1, x = a and x-axis is equal to 16/3, is
Options
A.1
B.2
C.-1
D.1/2
Solution
y = 8x2 - x5 = x2 (8 - x3)
case I a < 1
A =
or
or (a3 - 17) (a3 + 1) = 0
⇒ a = - 1 , a = (17)1/3 is not possible
case II a ∈ [1, 2]
A =
or 16a3 - a6 - 15 = 32
or a6 - 16a3 + 47 = 0
This equation is not satisfied by a = 1, a = 2
case III a > 2
There is no option
Hence one solution is - 1
case I a < 1
A =
or
or (a3 - 17) (a3 + 1) = 0
⇒ a = - 1 , a = (17)1/3 is not possible
case II a ∈ [1, 2]
A =
or 16a3 - a6 - 15 = 32
or a6 - 16a3 + 47 = 0
This equation is not satisfied by a = 1, a = 2
case III a > 2
There is no option
Hence one solution is - 1
Create a free account to view solution
View Solution Free