Find the area of the region bounded by the curve x*x=4y and the line x=4y-2.

Asked by Rishabh | 26th Nov, 2015, 09:03: AM

Expert Answer:

 
bold The bold space bold graphs bold space bold for bold space bold both bold space bold x to the power of bold 2 bold equals bold 4 bold y bold space bold and bold space bold x bold equals bold 4 bold y bold minus bold 2 bold space bold are bold space bold shown bold space bold above bold. bold Solving bold space bold both bold space bold equations bold comma bold space bold we bold space bold get bold space bold points bold space bold of bold space bold intersection bold space bold as bold space open parentheses bold minus bold 1 bold comma bold space bold 1 over bold 4 close parentheses bold space bold and bold space open parentheses bold 2 bold comma bold space bold 1 close parentheses bold. bold The bold space bold area bold space bold bounded bold space bold by bold space bold both bold space bold is bold space bold shown bold space bold by bold space bold the bold space bold shaded bold space bold part bold. bold One bold space bold rectangle bold space bold of bold space bold thickness bold space bold apostrophe bold dx bold apostrophe bold space bold is bold space bold shown bold space bold in bold space bold the bold space bold shaded bold space bold part bold. bold Area bold space bold of bold space bold this bold space bold rectangle bold space bold is bold space open parentheses bold y subscript bold 2 bold minus bold y subscript bold 1 close parentheses bold dx bold comma bold Area bold space bold of bold space bold the bold space bold bounded bold space bold region bold space bold is bold space bold found bold space bold by bold space bold integrating bold space bold the bold space bold above bold. bold Area bold space bold bounded bold equals bold integral subscript bold minus bold 1 end subscript superscript bold 2 open parentheses bold y subscript bold 2 bold minus bold y subscript bold 1 close parentheses bold dx bold equals bold integral subscript bold minus bold 1 end subscript superscript bold 2 open parentheses fraction numerator bold x bold plus bold 2 over denominator bold 4 end fraction bold minus bold x to the power of bold 2 over bold 4 close parentheses bold dx bold equals bold 1 over bold 4 open square brackets bold x to the power of bold 2 over bold 2 bold plus bold 2 bold x bold minus bold x to the power of bold 3 over bold 3 close square brackets subscript bold minus bold 1 end subscript superscript bold 2 bold equals bold 1 over bold 4 open square brackets bold 10 over bold 3 bold minus open parentheses bold minus bold 7 over bold 6 close parentheses close square brackets bold equals bold 1 over bold 4 open parentheses bold 9 over bold 2 close parentheses bold equals bold 9 over bold 8 bold space bold square bold space bold units

Answered by satyajit samal | 26th Nov, 2015, 12:24: PM

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