InterviewSolution
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InterviewSolution
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The value of ` int _ 3 ^ (4 ) sqrt((4- x ) (x - 3 )) dx ` isA. ` ( pi ) /( 16 ) `B. ` ( pi ) /( 8 ) `C. ` ( pi ) /( 4 ) `D. ` ( pi ) /( 2 ) ` |
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Answer» Correct Answer - B Let `I = int_ 3^ 4 sqrt ((4 - x ) ( x - 3)) dx ` ` = int _ 3 ^ 4 sqrt ( - x ^ 2 + 7x -12 ) dx ` ` = int_ 3 ^ 4 sqrt ( - ( x ^ 2 - 7x + (49)/ ( 4 ) - ( 49)/( 4 )) - 12 ) dx ` = ` int_ 3 ^ 4 sqrt ( - ( x - ( 7 ) /( 2 ) ) ^ 2 + ( 49 ) /( 4) - 12 ) dx ` ` = int _ 3 ^ 4 sqrt ( ( 1 ) / ( 4 ) - ( x - ( 7 ) / ( 2)) ^ 2 ) dx ` Let ` t = x - ( 7 ) /( 2 ) rArr dt = dx ` ` therefore ` Upper limit = ` ( 1) / ( 2 ) ` and lower limit = - ` ( 1 ) / (2 ) ` ` = int _ ( - 1//2 ) ^ ( 1//2 ) sqrt (( ( 1 )/( 2 ) ) ^ 2 - t ^ 2 ) dt ` ` = 2 int _ 0 ^ ( 1//2 ) sqrt(( ( 1 )/( 2))^ 2 - t ^ 2 ) dt ` `= 2 [ ( t ) /(2) sqrt (( 1 ) /( 4) - t ^ 2 ) + ( 1 ) /( 8 ) sin ^( - 1 ) 2t] _ ( 0) ^( 1//2 ) ` ` = 2 [0 + ( 1 ) /(8) xx ( pi ) / ( 2 )] ` ` = ( pi )/( 8 ) ` |
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