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Sir, Pls solve this question.

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Asked by rsudipto 8th December 2018, 2:55 PM
Answered by Expert
Answer:
Plotting
put x = 0 in x + sinx, you get 0
put x = pi, you get pi, which is  3.14
then x = 2pi, you get 2pi, which is 6.28
make a rough diagram
 
now draw a graph mirror to the blue one, which will be the inverse (red)
inverse graph can be made by taking mirror about y = x
 
Method 1
now this inverse graph is x - sinx graph.......this we can check by sub the values like pi , 2pi etc (OR refer to method 2)
 
 
The function f(x) = x+sin(x) and its inverse f '(x) = x-sin(x) are plotted in figure.
It can be seen that inverse of f(x) is reflection about the line y=x
 
Let us calculate area bounded between f(x) and iis inverse between x=0 and x=π .
 
begin mathsize 12px style integral subscript 0 superscript straight pi left parenthesis x plus sin space x space right parenthesis space minus space integral subscript 0 superscript straight pi left parenthesis x minus sin space x space right parenthesis space equals space integral subscript 0 superscript straight pi 2 space s in space x space space equals space 4 space s q. u n i t s end style
Hence area bounded between f(x) and iis inverse between x=0 and x= 2π is  8 sq. units
 
 
Method 2
 
we can find the area enclosed by x + sinx and x between 0 to pi (shaded part) and multiply it with 4 
 
 
begin mathsize 18px style integral subscript 0 superscript 2 straight pi end superscript open parentheses straight x plus sinx space minus space straight x close parentheses
equals integral subscript 0 superscript 2 straight pi end superscript open parentheses sinx space close parentheses
equals 2
now space there space are space 4 space such space figures
so space 2 cross times 4 equals 8 end style
 

Answered by Expert 9th December 2018, 3:43 AM
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