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Fundamental theorem of definite integral...

Fundamental theorem of definite integral :
If `I_(n)=int_(0)^(pi/4)tan^(n)dx` then `lim_(ntooo)n(I_(n)+I_(n+2))=.......`

A

1

B

`(1)/(2)`

C

`oo`

D

0

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The correct Answer is:
A
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. Definite integration as the limit of a sum : lim(ntooo)[(1)/(n)+(n^(...

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  2. Definite integration as the limit of a sum : lim(ntooo)[(1+(1)/(n^(2...

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  3. Fundamental theorem of definite integral : If I(n)=int(0)^(pi/4)tan^...

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  4. Fundamental theorem of definite integral : f(x)=int(2)^(x)(dt)/(sqrt...

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  5. Fundamental theorem of definite integral : f(x)=int(1)^(x)sqrt(2-t^(...

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  6. Fundamental theorem of definite integral : If int(sinx)^(1)t^(2)f(t)...

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  7. Fundamental theorem of definite integral : I=int(0)^(1)(sinx)/(sqrtx...

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  8. Fundamental theorem of definite integral : (d)/(dx)(F(x))=(e^(sinx))...

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  9. int(1)^(2)logxdx=..........

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  10. Fundamental theorem of definite integral : If int(0)^(k)(dx)/(1+4x^(...

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  11. int(3)^(5)(t^(2))/(t^(2)-4)dx=.............

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  12. int(0)^(pi)e^(x)cos2xdx=.............

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  13. Fundamental theorem of definite integral : int(-1)^(2)sqrt(5x+6)dx=....

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  14. Fundamental theorem of definite integral : int(0)^(pi/4)(sin^(9)x)/(...

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  15. Fundamental theorem of definite integral : int(0)^(pi)sqrt(1+4sin^(2...

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  16. Fundamental theorem of definite integral : int(0)^(pi/4)tan^(100)xdx...

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  17. Fundamental theorem of definite integral : int(a)^(b)(logx)/(x)dx=.....

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  18. Fundamental theorem of definite integral : int(0)^(pi/2)(cos2x)/((si...

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  19. int(0)^(5)sqrt(25-x^(2))dx=.............

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  20. Evaluation of definite integrals by subsitiution and properties of its...

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