Let f′(x)=192x3(2+sin4(nπ)) for all x∈R with f(1/2)=0. If m≤∫11/2f(x)dx≤M , then the possible values of m and M are
A
m=13,M=24
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
m=1/4,M=1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
m=−11,M=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
m=1,M=12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct options are Am=13,M=24 Dm=1,M=12 192x33<f′(x)<192x32 ⇒16(x4−116)<∫x12f(x)dx<24(x4−116) ⇒16(x55−x16)112<∫x12f(x)dx<24(x55−x16)112 ⇒2.6<∫x12f(x)dx<3.9 Hence, only possible option is D.