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The absolute value of int(10)^(19) (cos...

The absolute value of `int_(10)^(19) (cosx)/(1+x^(8))dx`, is

A

less than `10^(-7)`

B

more than `10^(-7)`

C

less than `10^(-8)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
For `x gt10`, we have
`|cosx|lt1 and 1 +x^(8)gt10^(8)rArr (1)/(1+x^(8))le10^(-8)`
`:. |underset(10)overset(19)int(cos x dx)/(1+x^(8))|leunderset(10)overset(19)int(|cosx|)/(1+x^(8))dxleunderset(10)overset(19)int10^(-8)=9xx10^(-8)lt10^(-7)`
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