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integral subscript 0 superscript 4{square root of x} dx    ;    [  { } in the sum represents fractional part function]

Asked by 24th March 2015, 6:18 PM
Answered by Expert
Answer:

Divide the interval from 0 to 1 and from 1 to 4.

integral subscript 0 superscript 4 open curly brackets square root of x close curly brackets d x equals integral subscript 0 superscript 1 open curly brackets square root of x close curly brackets d x plus integral subscript 1 superscript 4 open curly brackets square root of x close curly brackets d x equals integral subscript 0 superscript 1 square root of x d x plus integral subscript 1 superscript 4 open parentheses square root of x minus 1 close parentheses d x equals open square brackets fraction numerator x to the power of 3 divided by 2 end exponent over denominator 3 divided by 2 end fraction close square brackets subscript 0 superscript 1 plus open square brackets fraction numerator x to the power of 3 divided by 2 end exponent over denominator 3 divided by 2 end fraction minus x close square brackets subscript 1 superscript 4 T h e space a b o v e space e x p r e s s i o n space c a n space b e space s i m p l i f i e d space t o space g e t space t h e space f i n a l space r e s u l t.

Answered by Expert 24th March 2015, 6:41 PM
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