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# Sketch the graph of and evaluate

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## The given equation is y=| x+3 | and integral to be evaluated is ∫ −6 0 | x+3 | dx. To sketch the graph of the equation y=| x+3 |, put some values of x and find corresponding values of y. Make a table of values of y and x. xy −63 −52 −41 −30 −21 −1203 Plot the points from the above table and join them by straight lines. Figure (1) Figure (1) shows the graph of the equation y=| x+3 |. We have to evaluate the integral ∫ −6 0 | x+3 | dx. The absolute value function can be written as, y=−( x+3 ) −6≤x≤−3 y=( x+3 ) −3≤x≤0 Thus, the integral can be written as, ∫ −6 0 | x+3 | dx=− ∫ −6 −3 ( x+3 ) dx+ ∫ −3 0 ( x+3 )dx Integrate the above integral and apply the boundary conditions. ∫ −6 0 | x+3 | dx=− ∫ −6 −3 ( x+3 ) dx+ ∫ −3 0 ( x+3 ) dx =− [ x 2 2 +3x ] −6 −3 + [ x 2 2 +3x ] −3 0 =−[ ( −3 ) 2 2 +3( −3 )−( ( −6 ) 2 2 +3( −6 ) ) ]+[ ( 0 ) 2 2 +3( 0 )−( ( −3 ) 2 2 +3( −3 ) ) ] =−[ 9 2 −9−18+18 ]+[ − 9 2 +9 ] Further, solve the above equation. ∫ −6 0 | x+3 | dx=−[ 9 2 −9−18+18 ]+[ − 9 2 +9 ] =−[ − 9 2 ]+[ 9 2 ] =9 Thus, the value of integral ∫ −6 0 | x+3 | dx is 9 sq units.  Suggest Corrections  0      Similar questions
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