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Evaluate: underset(nrarrinfty)lim[(1/n^2...

Evaluate: `underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/(n^2))....+1/nsec^2(1)]`

A

1/2tan 1

B

tan 1

C

1/2 cosec1

D

1/2 sec1

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The correct Answer is:
A
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. find into^(pi/4) sinx dx=?

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  2. The value of int(-1)^3 [abs(x-2)+[x]] dx where [] denotes GiF is

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  3. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

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  4. integral 0 to pi xf(sinx) dx is equal to

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  5. If for x =0 af(x) +bf(1/x)=1/x-5 where a ne b then int1^2xf(x) dx is e...

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  6. If x^2f(x)+f(1/x)=2 for all x except at x=0 then int(1/3)^3 f(x) dx=

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  7. int0^(pi/2) e^x dx is equal to

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  8. The value of int1^2[2x^2-3] dx where [] denotes GIF is

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  9. The value of inta^b(abs(x))/x dx , altblt0 is :

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  10. If int[x]^(x+1) f(t)dt =[x] then th value of int(-2)^4 f(x) dx is equa...

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  11. Find the value of int0^2|x^2+2x-3|dx.

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  12. The value of int0^1.5 [x^2] dx is : where [x] denotes greatest integer...

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  13. Let In=int0^(pi/4)tan^nxdx, then 1/(I2+I4),1/(I3+I5), 1/(I4+I6), 1/(I5...

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  14. If int(-1)^4 f(x) dx =4 and int2^4[3-f(x)]dx=7 then the value of int(...

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  15. if I10=int0^(pi/2) x^(10) sinx dx then the value of I10 + 90 I8 is

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  16. If an= int0^(pi/4) cot^nx dx then a2+a4 , a3+a5 , a4+a6

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  17. The value of int(pi/6)^((5pi)/6)sqrt(4-4sin^2t)dt

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  18. int0^infty[2/lnx] dx where [] denotes the greatest integer equals

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  19. if int2^e [(1/logx)-(1/(logx)^2)] dx=a+(b/log2)' then

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  20. If I=abs(int2^6 (sinx dx)/(1+x^2) then

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