1 integration 0 of mod 5x-3

Asked by aadeshpdabre | 14th May, 2016, 02:33: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space i n t e g r a l I equals integral subscript 0 superscript 1 open vertical bar 5 x minus 3 close vertical bar d x W e space k n o w space t h a t comma open vertical bar 5 x minus 3 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell negative open parentheses 5 x minus 3 close parentheses space w h e n space 5 x minus 3 less than 0 rightwards double arrow x less than 3 over 5 end cell row cell open parentheses 5 x minus 3 close parentheses space w h e n space 5 x minus 3 greater or equal than 0 space rightwards double arrow x greater or equal than 3 over 5 end cell end table close space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis A l s o space w e space k n o w space t h a t integral subscript a superscript b f open parentheses x close parentheses d x space equals integral subscript a superscript c f open parentheses x close parentheses d x plus integral subscript c superscript b f open parentheses x close parentheses d x space space space comma space w h e r e space a less than c less than b H e r e comma space 0 less than 3 over 5 less than 1 T h u s comma integral subscript 0 superscript 1 open vertical bar 5 x minus 3 close vertical bar d x space equals integral subscript 0 superscript 3 over 5 end superscript open vertical bar 5 x minus 3 close vertical bar d x plus integral subscript 3 over 5 end subscript superscript 1 open vertical bar 5 x minus 3 close vertical bar d x space space space space space space space space space space space space space space space space space space space equals integral subscript 0 superscript 3 over 5 end superscript minus open parentheses 5 x minus 3 close parentheses d x plus integral subscript 3 over 5 end subscript superscript 1 open parentheses 5 x minus 3 close parentheses d x space space space space space space space space space space space space b y space d e f i n i t i o n space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis space space space space space space space space space space space space space space space space space space space equals open square brackets 3 x minus fraction numerator 5 x squared over denominator 2 end fraction close square brackets subscript 0 superscript 3 over 5 end superscript plus open square brackets fraction numerator 5 x squared over denominator 2 end fraction minus 3 x close square brackets subscript 3 over 5 end subscript superscript 1 space space space space space space space space space space space space space space space space space space space equals open square brackets 3 cross times 3 over 5 minus fraction numerator 5 open parentheses 3 over 5 close parentheses squared over denominator 2 end fraction close square brackets plus open square brackets 5 over 2 minus fraction numerator 5 open parentheses 3 over 5 close parentheses squared over denominator 2 end fraction minus 3 plus 3 cross times 3 over 5 close square brackets space space space space space space space space space space space space space space space space space space space equals open square brackets 3 cross times 3 over 5 minus fraction numerator 5 open parentheses 3 over 5 close parentheses squared over denominator 2 end fraction close square brackets plus open square brackets 5 over 2 minus fraction numerator 5 open parentheses 3 over 5 close parentheses squared over denominator 2 end fraction minus 3 plus 3 cross times 3 over 5 close square brackets space space space space space space space space space space space space space space space space space space space equals open square brackets 9 over 5 minus 9 over 10 close square brackets plus open square brackets fraction numerator negative 1 over denominator 2 end fraction plus 9 over 10 close square brackets space space space space space space space space space space space space space space space space space space space equals 13 over 10

Answered by Vimala | 14th May, 2016, 03:55: PM

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