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Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral `int_(0)^(5)[x]{x}dx` is -A. `5//2`B. 5C. `34.5`D. `35.5` |
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Answer» Correct Answer - B `int_(0)^(5)[x]{x}dx=int_(0)^(5)[x](x-[x])dx=int_(0)^(1)0.dx+int_(1)^(2)1.(x-1)dx+int_(2)^(3)2(x-2)dx+int_(3)^(4)3(x-3)dx+int_(4)^(5)4(x-4)dx` `(((x-1)^(2))/(2))^(2)+2(((x-2)^(2))/(2))_(2)^(3)+3(((x-3)^(2))/(2))_(3)^(4)+4(((x-4)^(2))/(2))_(4)^(5)` `(1)/(2)+(2)/(2)+(3)/(2)+(4)/(2)` = 5 |
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