CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The value of integral 21[[x]1+x2]dx, where []denotes the greatest integer function, is equal to

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1
We know, [x]=0,x[0,1)
For x[1,2), [x]=1
[x]1+x2=11+x2
Clearly, 11+x2<1,x[1,2)
[[x]1+x2]=0
For x[1,0), [x]=1
[[x]1+x2]=[11+x2]
In the interval x[1,0)
1211+x2<11211+x2>1
[[x]1+x2]=1x[1,0)
Thus, the given integral is
I=01(1)dx+10(0)dx+21(0)dxI=1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon