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The series 1 + 1/2 + 1/3 +…..+ 1/n can b...

The series `1 + 1/2 + 1/3 +…..+ 1/n` can be expressed by the definite integral

A

`int_(0) ^((pi)/(2)) tan ((theta)/(2)) (1- cos ^(n) theta) d theta`

B

`int_(0) ^((pi)/(2)) cot ((theta)/(2)) (1- cos ^(n) theta) d theta`

C

`int_(0) ^((pi)/(4)) cot ((theta)/(2)) (1+cos ^(n) theta) d theta`

D

`int_(0) ^((pi)/(4)) tan ((theta)/(2)) (1+cos ^(n) theta) d theta`

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-INTEGRALS -EXERCISE-1 CONCEPT BUILDER
  1. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

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  2. The value of int(0) ^(1) (dx )/( e ^(x) + e) is equal to

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  3. The value of int(-1)^(3)(|x|+|x-1|) dx is equal to

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  4. The value of int(-pi) ^(pi) (sin ^(2) x)/( 1 + 7 ^(x)) dx= is equal to

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  5. int ( log 1//2 ) ^( log 2) sin { (e ^(x) -1)/( e ^(x ) +1 )}dx equals

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  6. Let f (x) = x^(2) -2. If int (3) ^(6) f (x)dx =3f (c ) for some c in (...

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  7. int0^pix(sin^4xcos^4x)dx

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  8. If I(n) = int (0)^(pi//4) tan^(n) theta " " d theta, "then "I(8)+I(6)=

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  9. In=int0^(pi//4) tan^n x\ dx, then lim(ntooo) n\ [In + I(n+2)] is equal...

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  10. What is int tan^(2) x sec^(4) x dx equal to ?

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  11. int(0)^(pi//2) sin^(2) x cos ^(3) x dx

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  12. If int0^ooe^(-ax)dx=1/a, then int0^oo(x^n)e^(-ax)dx is

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  13. If I(m,n)= overset(1)underset(0)int x^(m) (ln x)^(n)dx then I(m,n) i...

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  14. What is the limiting value of the expression ({(n +1) (n+2).....(2n)...

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  15. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

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  16. The limit, when the tends to infinity, of the series (sqrtn)/( sqrt ...

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  17. The series 1 + 1/2 + 1/3 +…..+ 1/n can be expressed by the definite in...

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  18. lim(n - >oo) {1/(2n+1)+1/( 2n +2) +....... 1/(2n +n)} is equal to

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  19. Evaluate: int(1+2x+3x^2+4x^3+)dx ,(<|x|<1)

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  20. If Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-4))++1/(sqrt(3n^2+2n-1)),n ...

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