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$integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x$

$\frac{100}{π}$
$\frac{200}{π}$
$100 π$
$200 π$

hint Hint:

We are aware that differentiation is the process of discovering a function's derivative and integration is the process of discovering a function's antiderivative. Thus, both processes are the antithesis of one another. Therefore, we can say that differentiation is the process of differentiation and integration is the reverse. The anti-differentiation is another name for the integration.
Here we have given: $integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x$ and we have to integrate it. We will use the function method to find the answer.

The correct answer is: $200 over pi$

Now we have given the function as $integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x$ . Here the lower limit is 0 and upper limit is 1. We know that a repeating action that happens at regular intervals is known as a periodic function. So, after a predetermined amount of time, the function returns to its starting place.
We have:
$integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x W e space w i l l space u s e colon space x minus left square bracket x right square bracket equals left curly bracket x right curly bracket comma space w h e r e space left curly bracket x right curly bracket space i s space f r a c t i o n a l space p a r t space f u n c t i o n. integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x equals integral subscript 0 superscript 100 sin invisible function application pi left curly bracket x right curly bracket d x N o w comma space f left parenthesis left curly bracket x right curly bracket right parenthesis space i s space a space p e r i o d i c space f u n c t i o n space w i t h space p e r i o d space 1. space S o space w e space c a n space w r i t e space i t space a s colon integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x equals 100 cross times integral subscript 0 superscript 1 sin invisible function application pi left curly bracket x right curly bracket d x integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x equals 100 cross times integral subscript 0 superscript 1 sin invisible function application pi x d x integral subscript 0 superscript 100 sin invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis pi d x equals fraction numerator negative 100 over denominator straight pi end fraction cross times left parenthesis cos space πx right parenthesis subscript 0 superscript 1 space Now space substituting space the space limits comma space we space get colon integral subscript 0 superscript 100 sin invisible function application left parenthesis straight x minus left square bracket straight x right square bracket right parenthesis πdx equals fraction numerator negative 100 over denominator straight pi end fraction cross times left parenthesis cos space straight pi space minus cos space 0 space right parenthesis subscript 0 superscript 1 integral subscript 0 superscript 100 sin invisible function application left parenthesis straight x minus left square bracket straight x right square bracket right parenthesis πdx equals fraction numerator negative 100 over denominator straight pi end fraction cross times left parenthesis negative 1 space minus space 1 space right parenthesis integral subscript 0 superscript 100 sin invisible function application left parenthesis straight x minus left square bracket straight x right square bracket right parenthesis πdx equals 200 over straight pi$

So here we used the concept of integrals of special functions and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the substitution method to solve. The integral of the given function is $integral subscript 0 superscript 100 sin invisible function application left parenthesis straight x minus left square bracket straight x right square bracket right parenthesis πdx equals 200 over straight pi$ .

$integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x equals$

So here we used the concept of integrals of special functions and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the modulus function to solve. The integral of the given function is $integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x equals 2$

$integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x equals$

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The correct answer is:

Now we have given the function as . Here the lower limit is 0 and upper limit is 1. We know that a repeating action that happens at regular intervals is known as a periodic function. So, after a predetermined amount of time, the function returns to its starting place.We have:

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The correct answer is: $200 over pi$

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Which of the following plots represents correctly variation of equivalent conductance $open parentheses logical and close parentheses$ with dilution for a strong electrolyte ?

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