-1019sin x d x-1-x108- is less thenA- 10-10B- 10-11C- 10-7D- 10-9

The correct option is B 10^ 11|∫_10^19sin x dx/1+x^8|≤∫_10^19|sin x/1+x^8|dx ≤∫_10^191/1+x^8dx lt; ∫_10^19dx/x^8 = 1/7[x^ 7]_10^19 =1/710^ 7 1/719^ 7 lt;1 ...

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Byju's Answer

Standard XII

Mathematics

Property 4

∫1019sin x d ...

Question

$| \int_{10}^{19} \frac{s i n x d x}{1 + x^{8}} | i s l e s s t h e n$

10^{- 10}

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10^{- 11}

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10^{- 7}

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10^{- 9}

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Solution

The correct option is B $10^{- 11}$
$| \int_{10}^{19} \frac{s i n x d x}{1 + x^{8}} | \leq \int_{10}^{19} | \frac{s i n x}{1 + x^{8}} | d x$
$\leq \int_{10}^{19} \frac{1}{1 + x^{8}} d x < \int_{10}^{19} \frac{d x}{x^{8}}$
$= \frac{- 1}{7} [x^{- 7}]_{10}^{19}$
= $\frac{1}{7} 10^{- 7} - \frac{1}{7} 19^{- 7} < \frac{1}{7} 10^{- 7} < 10^{- 7}$

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|∫1910sin x dx1+x8| is less then

The correct option is B 10−11|∫1910sin x dx1+x8|≤∫1910|sin x1+x8|dx ≤∫191011+x8dx<∫1910dxx8 =−17[x−7]1910 =1710−7−1719−7<1710−7<10−7

$| \int_{10}^{19} \frac{s i n x d x}{1 + x^{8}} | i s l e s s t h e n$