wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The number of continuous functions f:[0,1]R that satisfy
10xf(x) dx=13+1410(f(x))2 dx

A
0
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
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Infinity
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1
10xf(x) dx=13+1410(f(x))2 dx13=10(f(x)2)2xf(x) dx10(f(x)2x)2 dx10x2 dx=1310(f(x)2x)2 dx=0
(f(x)2x)2=0
f(x)=2x
Only one function exists.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon