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Column I, Column II If f(x) is an int...

Column I, Column II If `f(x)` is an integrable function for `x in [pi/6,pi/3]a n d` `I_1=int_(pi/6)^(pi/3)sec^2thetaf(2sin2theta)dtheta,a n d` `I_2=int_(pi/6)^(pi/3)"c o s e c"^2thetaf(2sin2theta)dtheta,t h e n(I_1)/(I_2)=` , p. 3 If `f(x+1)=f(3+x)AAx ,` and the value `ofint_a^(a+b)f(x)dxi sin d e p e n d e n tofa ,` then the value of `b` can be, q. 1 The value of `int_0^1(tan^(-1)[x^2])/(tan^(-1)[x^2]+tan^(-1)[25+x^2-10 x])` , r. 2 `(d)IfIint_0^2sqrt(x+sqrt(x+sqrt(x+oo)))dx(w h e r ex` `>0),t h e n[I]` is equal to (where [.] denotes the greatest integer function), s. 4

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If f(x) is an integrable function on [(pi)/(6),(pi)/(3)] and I_(1)=int_(pi//6)^(pi//3) sec^(2)thetaf(2 sin 2theta)d theta" and "I_(2)=int_(pi//6)^(pi//3) "cosec"^(2)theta f(2 sin2theta)d theta , then

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x...

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  2. Consider the polynomial f(x)=a x^2+b x+cdot If f(0)=0,f(2)=2, then the...

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  3. Column I, Column II If f(x) is an integrable function for x in [pi/...

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  4. STATEMENT 1: If f(x) is continuous on [a , b] , then there exists a po...

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  5. The value of the definite integral, int0^(pi/2) (sin5x)/sinx dx is

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  6. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >...

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  7. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

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  8. If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ...

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  9. int0^1(tan^(-1)x)/x dx is equals to (a) int0^(pi/2)(sinx)/x dx (b)...

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  10. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

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  11. L e tI1=int0^1(e^xdx)/(1+x) a n dI2=int0^1(x^2dx)/(e^(x^3)(2-x^3))dot ...

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  12. int(sintheta)^(costheta)f(xtantheta)dx(w h e r etheta!=(npi)/2,n in I...

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  13. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

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  14. The value of int0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (...

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  15. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)"is equal to" 3/5 ...

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  16. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  17. For any real number x, let [x] denote the largest integer less than or...

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  18. evaluate: int0^(pi/4)2tan^3xdx is

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  19. If f is continuous function and F(x)=int0^x((2t+3)*intt^2f(u)d u)dt , ...

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  20. Let f^(prime)(x)=(192 x^3)/(2+sin^4pix)fora l lx in Rw i t hf(1/2)=0....

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