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Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0...

Let `I=int_0^1(sin)/(sqrt(x))dx"and"J=int_0^1(cosx)/(sqrt(x))dx` Then which one of the following is true? (1) `I >2/3"and"j >2` (2) `I<2/3"and"j<2` (3) `I<2/3"and"j >2` (4) `I >2/3"and"j<2`

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BANSAL-INTEGRALS-All Questions
  1. int(-1)^1(dx)/(1+x^2)

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  2. int0^1(dx)/(1-x^2)\

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  3. int2^3(dx)/(1-x^2)

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  4. int1^2(dx)/(x\ sqrt(x^2-1))

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  5. Let f be a non-negative function defined on the interval [0,1]dot If i...

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  6. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

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  7. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

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  8. The value of (lim)(x->0)1/(x^3)int0^x(t ln(1+t))/(t^4+4)dt is a.0 b. 1...

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  9. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

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  10. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  11. For any real number x ,l e t[x] denote the largest integer less than o...

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  12. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

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  13. The value of the integral int(pi//2)^(pi//2)(x^2ln(pi+x)/(pi-x))cos...

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  14. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

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  15. Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0^1(cosx)/(sqrt(x))dx Then w...

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  16. int0^pi[cotx]dx , where [.] denotes the greatest integer function, is ...

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  17. Let p(x) be a function defined on R such that (lim)(x->oo)(f(3x))/(...

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  18. Statement 1: The value of the integral int(pi//6)^(pi//3)(dx)/(1+sqrt(...

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  19. The value of int0^1(8log(1+x))/(1+x^2)dx is a.pilog2 b. \ pi/8log2 c.\...

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  20. If g(x)=int0^x cos4t\ dt ,\ t h e n\ g(x+pi) equals a.g(x)-g(pi) b. \ ...

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