1.

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 ?

Answer»

`underset(0)overset(1)inte^(-x)f(x)dxle10`
`underset(0)overset(1)INT(f(x))/((1+x)^(2))dxle10`
`-10leunderset(0)overset(1)intsin(100X)fxle10`
`underset(0)overset(1)INTF(x)^(2)dxle100`

Solution :`:. 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.


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