Indefinite Integration 3 Question 4

4. Let f be a non-negative function defined on the interval [0,1]. If 0x1(f(t))2dt=0xf(t)dt,0x1 and f(0)=0, then (2009) (a) f12<12 and f13>13

(b) f12>12 and f13>13

(c) f12<12 and f13<13

(d) f12>12 and f13<13

Show Answer

Answer:

Correct Answer: 4. (c)

Solution:

  1. Given 0x1f(t)2dt=0xf(t)dt,0x1

Differentiating both sides w.r.t. x by using Leibnitz’s rule, we get

1f(x)2=f(x)f(x)=±1f(x)2f(x)1f(x)2dx=±dxsin1f(x)=±x+c Put x=0sin1f(0)=cc=sin1(0)=0[f(0)=0]

f(x)=±sinx but f(x)0,x[0,1]f(x)=sinx

sinx<x,x>0sin12<12 and sin13<13f12<12 and f13<13



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक