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`int_(-1)^1(dx)/(1+x^2)`

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int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

int_(0)^(1)(dx)/((1+x^(2))

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int_(0)^(1)(dx)/(x^((1)/(2))(1-x)^((1)/(2)))

If int_(0)^(1)(dx)/((1+x)sqrt(1-x^(2)))=(a)/(b) , then

Let I_(1) = int_(0)^(pi//4)1/((1+tanx)^(2))dx , I_(2) = int_(0)^(1)(dx)/((1+x)^(2)(1+x^(2))) Then find the value of (I_(1))/(I_(2)) .

int_(-1)^(1)(1-x^(2))/(1+x^(2))dx is

(i) int_0^1 (dx)/sqrt(1-x^2) (ii) int_0^1 (dx)/sqrt(1+x^2) (iii) a int_1^sqrt3 (dx)/(1+x^2) b int_0^1 (dx)/(1+x^2) (iv) int_0^(2//3) (dx)/(4+9x^2) (v) int_0^1 x/(x^2+1)dx (vi) int_2^3 x/(x^2+1) dx

BANSAL-INTEGRALS-All Questions
  1. Find the value of (5050int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^...

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  2. (lim)(x->4)(int2sec^2\ f(t)dt)/(x^2-(pi^2)/(16)) equals a.8/pif(2) b. ...

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  3. int(-1)^1(dx)/(1+x^2)

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

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

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

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

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

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

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  10. 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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  11. 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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  12. Let f be a real-valued function defined on the inverval (-1,1) such th...

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

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

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

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

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

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

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

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