The absolute value of ∫1019 sin⁡x1+x8dx is

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less than 10−7

more than 10−7

equal to 10−7

none of these

answer is A.

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Detailed Solution

For x≥10, we have |sin⁡x|≤1 and 1+x8≥108⇒11+x8≤10−8Therefor1∫1019 sin⁡x1+x8dx∣≤∫1019 |sin⁡x|1+x8dx≤∫1019 10−8dx=910−8<10−7

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