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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^(15)[x]dx`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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

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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. The value of int0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(sin x))dx is p...

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  8. int0^pi1/(1+sinx)dx equals a. 0 b. 1//2 c. 2 d. 3//2

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

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

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

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

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  13. 36/piint(pi//6)^(pi//3)(dx)/(1+sqrt(cotx)) equals to

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  14. 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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  15. int1^elogx\ dx= a. 1 b. e-1 c. e+1 d. 0

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

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  17. The value of int0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -...

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  18. If int0^a1/(1+4x^2)dx=\ pi/8 , then a equals a.pi/2 b. pi/4 c. 1/2 d. ...

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  19. int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0^1x^2f(x)dx=a^2,\ t h e n\ int...

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  20. The value of int(-pi)^pisin^3xcos^2x\ dx\ is a.(pi^4)/2 b. (pi^4)/4 c...

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