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If [dot]a n d\ {dot} denote respectively...

If `[dot]a n d\ {dot}` denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: `int_0^2[x]dx`

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` x=0, x=2`
`[x] = {(0 ; 0 le x lt 1), (1; 1 le x lt 2):}`
`=int_0^1 0*dx + int_1^2 1*dx`
`=[x]_1^2`
`=(2-1)`
`=1`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
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  2. The value of int-2^2 (ax^3+bx+c)dx depends on (A) the value of b (B) t...

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  3. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  4. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  5. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  6. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  7. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  8. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  9. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  10. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  11. The value of int0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is ...

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  12. int0^(pi/2) 1/(1+sinx)dx equals 0 b. 1//2 c. 2 d. 3//2

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  13. int0^oo1/(1+e^x)dx equals a. log2-1 b. log2 c. log4-1 d. log2

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  14. The value of int0^(2pi)sqrt(1+sin (x/2)dx is 0 b. 4 c. 2 d. 8

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  15. int0^(pi^2//4)(sinsqrt(x))/(sqrt(x))dx equals a. pi^2//8 b. pi//4 ...

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  16. int0^(pi//2)1/(2+cos\ x)dx equals 1/3tan^(-1)(1/(sqrt(3))) b. 2/(sqrt(...

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  17. 36/piint(pi//6)^(pi//3)(dx)/(1+sqrt(cotx)) equals to

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  18. Given that int0^oo(x^2)/((x^2+a^2)(x^2+b^2)(x^2+c^2))dx=pi/(2(a+b)(b+c...

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  19. int1^elogx\ dx= 1 b. e-1 c. e+1 d. 0

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  20. int1^(sqrt(3))1/(1+x^2)dx is equal to pi/(12) b. pi/4 c. pi/6 d. pi/3

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