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If (x) donotes the greates integer lex,...

If (x) donotes the greates integer `lex,` then the value of `int_(4)^(10)([x^(2)])/([x^(2)-28x+196]+[x^(2)])` dx is -

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`I=underset(4)overset(10)int([x^(2)]dx)/([(14-x^(2))]+[x^(2)])` by using propery
`I=underset(4)overset(10)intf(x)dx=underset(a)overset(b)intf(a+b-x)dx`
also, `I=underset(4)overset(10)int([4+10-x^(2)]dx)/([(14-(14-x))^(2)]+[(14-x^(2))])`
`2Iunderset(4)overset(10)int(([x]^(2))/([(14-x)]^(2)+[x]^(2))+ [(14-x)^(2)]/([x^(2)]+[(14-x)^(2)]))dx`
`=underset(4)overset(10)int1.dxrArr1=3`
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