The maximum area bounded by the curves y2=4ax,y=ax and y=xa(1<a≤2)
A
84
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
64
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
50
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
48
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A84 The curves are y2=4ax and y=ax. At their point of intersection a2x2=4ax⇒ax=4,x=0x=4a⇒A(4a,4)
Similarly for y2=4ax and y=xa, x2a2=4ax ⇒x=4a3 ⇒B(4a3,4a2)
Area(OAB)=4/a∫0(ax−xa)dx+4a3∫4/a(√4ax−xa)dx
A=83(a5−1a)
dAda=83⋅(5a4+1a2)>0∀a ⇒A(a) is increasing function ∴Amax=83(a5−1a)∣∣∣a=2=83(32−12)=84sq. units