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Find the value of int(-1)^1[x^2+{x}]dx ,...

Find the value of `int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot}` denote the greatest function and fractional parts of `x ,` respectively.

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The correct Answer is:
`(3-sqrt(5))/2`
`int_(-1)^(1)[x^(2)+{x}]dx=int_(-1)^(0)[x^(2)+x+1]dx+int_(0)^(1)[x^(2)+x]dx`
`=0+int_(0)^((sqrt(5)-1)/2)0dx+int_((sqrt(5)-1)/2)^(1)1dx`
`=(3-sqrt(5))/2`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
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  9. Find the value of int(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx.

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  11. Find the value of int0^1x(1-x)^ndx

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  13. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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  14. Find the value of int(0)^(pi//2)sin2xlogtanxdx.

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  15. The value of int-pi^pi cos^2x/[1+a^x]dx, a > 0 is

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  16. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

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  17. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  18. Find the value of int(0)^(2pi)1/(1+tan^(4)x)dx

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  19. int0^(2pi)sin^(100)xcos^(99)x dx equals to ?

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