Let `f: [0,1]rarr[0,oo]` be a continuous function such that `int_(0)^(1) f(x)dx=10`. Which of the following statements is NOT necessarily true ?

Question

Let `f: [0,1]rarr[0,oo]` be a continuous function such that `int_(0)^(1) f(x)dx=10`. Which of the following statements is NOT necessarily true ?

Let `f: [0,1]rarr[0,oo]` be a continuous function such that `int_(0)^(1) f(x)dx=10`. Which of the following statements is NOT necessarily true ?
A. `underset(0)overset(1)inte^(-x)f(x)dxle10`
B. `underset(0)overset(1)int(f(x))/((1+x)^(2))dxle10`
C. `-10leunderset(0)overset(1)intsin(100x)fxle10`
D. `underset(0)overset(1)intf(x)^(2)dxle100`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
`:. F(x) le0`
`underset(0)overset(1)intf(x)^(2)dxle100` not necessarily ture.
because `(f(x))^(2)` can take very high was values then are bounded by `(f(x))^(2),` xaxis & x=0 to 1 may cross 100.

4 views Answered 2023-02-05 15:29