AP EAMCET202318 May 2023Evening ShiftMathematicsDefinite IntegrationActual
Assertion (A): _ 2 ^ 3 2 [2 x] d x=0 , where [.] denotes the greatest integer function Reason (R) : 2 x is a decreasing function in [ 2 , 3 2 ]
Options
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true, R is false
- DA is false, R is true
Correct answer
D. A is false, R is true
Step-by-step solution
aligned & (A) _ 2 ^ 3 2 [2 x] d x=2 _ 2 ^ 3 2 [ x] d x & =2 [ _ 2 ^ 0 dx + _ ^ 2 (-1) dx ] & aligned aligned & =2 ([- x ]_ ^ 2 )=2 [- 2 + ]=2 2 & _ 2 ^ 3 2 [2 x] dx = 0 aligned A is false (R) From the graph of 2 x , it is clear that 2 x is decreasing function in the interval [ 2 , 3 2 ]