The absolute value of _ 10 ^ 19 , , ,x 1 , , + , , x^8 is less th… - Vidyadip

MCQ

The absolute value of $\int\limits_{10}^{19} {\,\,\frac{{\sin \,x}}{{1\,\, + \,\,{x^8}}}} $ is less than :

A
$10^{ -10}$
B
$10^{ -11}$
✓
$10 ^{-7}$
D
$10^{ -9}$

✓

Answer

Correct option: C.

$10 ^{-7}$

c
$\left| {\int\limits_{10}^{19} {\,\,\frac{{\sin \,x}}{{1\,\, + \,\,{x^8}}}} } \right|$ $\le$ $\int\limits_{10}^{19} {\,\,\frac{{\left| {\sin \,x} \right|}}{{1\,\, + \,\,{x^8}}}}$ $dx$ $\le$ $\int\limits_{10}^{19} {\,\,\frac{{dx}}{{1\,\, + \,\,{x^8}}}}$ $<$ $\int\limits_{10}^{19} {\,\,\frac{{dx}}{{{x^8}}}}$ $=$ $\left[ {\frac{{{x^{ - 7}}}}{{ - \,7}}} \right]_{10}^{19}$ $= -\frac{1}{7} [19 ^{-7} - 10 ^{-7}]$ $= \frac{1}{7} [10 ^{-7} - 19 ^{-7}]$ $< 10 ^{-7}$

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