The value of integral -1-2-sin1-x-x2 d x-

The correct option is D 1Put t=1/x⇒ dt= 1/x^2dx as t=π/2 and π ∴∫_1/π^2/πsin ( 1/x )/x^2= ∫_π/2^π sin t dt= [cos t]_π/2^π = [ cos π cos ( π/2 ) ]=1 ...

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Standard XII

Mathematics

Property 1

The value of ...

Question

The value of integral $\int_{\frac{1}{π}}^{\frac{2}{π}} \frac{s i n (\frac{1}{x})}{x^{2}} d x =$

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Solution

The correct option is C 1
$P u t t = \frac{1}{x} \Rightarrow d t = - \frac{1}{x^{2}} d x a s t = \frac{π}{2} a n d π ∴ \int_{\frac{1}{π}}^{\frac{2}{π}} \frac{s i n (\frac{1}{x})}{x^{2}} = - \int_{\frac{π}{2}}^{π} s i n t d t = - [c o s t]_{\frac{π}{2}}^{π} = - [c o s π - c o s (\frac{π}{2})] = 1$

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The value of integral ∫2π1πsin(1x)x2dx=

The correct option is C 1Put t=1x⇒dt=−1x2dx as t=π2 and π∴∫2π1πsin(1x)x2=−∫ππ2 sin t dt=−[cos t]ππ2=−[cos π−cos(π2)]=1

The value of integral $\int_{\frac{1}{π}}^{\frac{2}{π}} \frac{s i n (\frac{1}{x})}{x^{2}} d x =$