If A=4∫1{x−0.4}dx, where {x} is a fractional part function, then the value of A is
A
13
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
6.3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1.5
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
7.5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C1.5 Let I=4∫1{x−0.4}dx
Put x−0.4=t⇒dx=dt x=1⇒t=0.6x=4⇒t=3.6
Now, I=3.6∫0.6{t}dt=0.6+3∫0.6{t}dt
Using the property: a+nT∫af(x)dx=nT∫0f(x)dx ⇒I=31∫0{t}dt=31∫0tdt∴I=3×12=1.5