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

0
1
2
$π$

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: $integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x$ and we have to integrate it. We will use the substitution method to find the answer.

The correct answer is: 2

Now we have given the function as $integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x$ . Here the lower limit is $fraction numerator negative straight pi over denominator 2 end fraction$ and upper limit is $straight pi over 2$ .
The integral of |x| depends on the domain in which it is being integrated.
For x>0, |x| = x.
For x<0, |x| = -x.
We have:
$integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x N o w space w e space w i l l space w r i t e space m o d space o f space x space i n space p o s i t i v e space a n d space n e g a t i v e space p a r t comma space w e space g e t colon integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x equals negative integral subscript negative pi divided by 2 end subscript superscript 0 sin space x d x plus integral subscript 0 superscript pi divided by 2 end superscript sin space x d x N o w space i n t e g r a t i n g space i t comma space w e space g e t colon left parenthesis cos space x right parenthesis subscript negative pi divided by 2 end subscript superscript 0 minus left parenthesis cos space x right parenthesis subscript 0 end subscript superscript pi divided by 2 end superscript S u b s t i t u t i n g space t h e space l i m i t s comma space w e space g e t colon left parenthesis cos space 0 space minus space cos space left parenthesis fraction numerator negative pi over denominator 2 end fraction right parenthesis right parenthesis minus left parenthesis cos space pi over 2 minus cos space 0 right parenthesis left parenthesis 1 minus 0 right parenthesis minus left parenthesis 0 minus 1 right parenthesis integral subscript negative pi divided by 2 end subscript superscript pi divided by 2 end superscript sin invisible function application vertical line x vertical line d x equals 2$ .

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

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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The correct answer is: 2

Now we have given the function as . Here the lower limit is and upper limit is .The integral of |x| depends on the domain in which it is being integrated.For x>0, |x| = x.For x<0, |x| = -x.We have:.

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0
1
2
$π$

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

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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if $a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent equals a b plus b c plus c a$ then the triangle is

A sphere of mass $m$ is held between two smooth inclined walls. For $s i n invisible function application 37 to the power of ring operator end exponent equals 3 divided by 5$ . The normal reaction of the wall(2) is equal to:

A sphere of mass $m$ is held between two smooth inclined walls. For $s i n invisible function application 37 to the power of ring operator end exponent equals 3 divided by 5$ . The normal reaction of the wall(2) is equal to:

Two light strings connect three particles of masses $m subscript 1 end subscript comma m subscript 2 end subscript$ and $m subscript 3 end subscript$ . If $m subscript 3 end subscript$ moves with an acceleration a as shown in the figure, the ratio of tension in the strings 1 and 2 is

Two light strings connect three particles of masses $m subscript 1 end subscript comma m subscript 2 end subscript$ and $m subscript 3 end subscript$ . If $m subscript 3 end subscript$ moves with an acceleration a as shown in the figure, the ratio of tension in the strings 1 and 2 is

Two forces $stack F with rightwards arrow on top subscript 1 end subscript$ and $stack F with rightwards arrow on top subscript 2 end subscript$ act at the ends of a massless string opposite to each other. Then

Two forces $stack F with rightwards arrow on top subscript 1 end subscript$ and $stack F with rightwards arrow on top subscript 2 end subscript$ act at the ends of a massless string opposite to each other. Then