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If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt...

If `I_(n)=int_(0)^(pi//4) tan^(n)x dx, (ngt1` is an integer ), then (a) `I_(n)+I_(n-2)=1/(n+1)` (b) `I_(n)+I_(n-2)=1/(n-1)` (c) `I_(2)+I_(4),I_(6),…….` are in H.P. (d) `1/(2(n+1))ltI_(n)lt1/(2(n-1))`

A

`I_(n)=I_(n-2)`

B

`I_(n)+I_(n-2)=(1)/(n-1)`

C

`I_(n)-I_(n-2)=(1)/(n-1)`

D

none of these

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of lim(n to oo) {(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))...(2)}^(1...

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  2. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  3. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I(...

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  4. If Im=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then

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  5. If I(m)=int(0)^(oo) e^(-x)x^(n-1)dx, "then" int(0)^(oo) e^(-lambdax) x...

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  6. If I(mn)=int(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m, n epsilon I, m,n ge 0 ), t...

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  7. Find the points of maxima /minima of int(0)^(x^(2))(t^(2)-5t+4)/(2+e^(...

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  8. Evaluate the following definite integral: int(-pi)^(pi)(2x(1+sinx))/(1...

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  9. The value of the inntegral int(alpha)^(beta) (1)/(sqrt((x-alpha)(beta-...

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  10. The value of the integral int(alpha)^(beta) sqrt((x-alpha)(beta-x))dx,...

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  11. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

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  12. The value of integral int(1)^(e) (log x)^(3)dx , is

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  13. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  14. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  15. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

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  16. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

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  17. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

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  18. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

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  19. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

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  20. Let I= int(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral ...

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