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If an= int0^(pi/4) cot^nx dx then a2+a4 ...

If `a_n= int_0^(pi/4) cot^nx dx` then `a_2+a_4 , a_3+a_5 , a_4+a_6`

A

G.P.

B

A.P.

C

H.P.

D

none of these

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The correct Answer is:
C
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Consider I_1=int_0^(pi//4)e^(x^2)dx ,I_2=int_0^(pi//4)e^x dx ,I_3=int_0^(pi//4)e^(x^2)cosxdx , I_4=int_0^(pi//4)e^(x^2)sinxdx . STATEMENT 1 : I_2> I_1> I_3> I_4 STATEMENT 2 : For x in (0,1),x > x^2a n dsinx >cosx .

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. 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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  2. if I10=int0^(pi/2) x^(10) sinx dx then the value of I10 + 90 I8 is

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

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

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

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

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

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  8. Let f(x) =int(-1)^x abs(x+1) dx then

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  9. If a continous function f satisfies int0^f(x) t^2 dt=x^2(1+x) for all ...

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  10. The value of int0^(sin^2x)sin^(-1)(sqrtt)dt+int0^(cos^2x)cos^(-1)(sqrt...

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  11. A line tangent to the graph of the function y=f(x) at the pointx =a fo...

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  12. The value of int0^(pi/2)log(tanx)dx is

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  13. int(pi/2)^(3pi/2) [2sinx]dx is equal to [x] denotes the greatest integ...

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  14. The value of the integral int0^3 dx/((sqrt(x+1) +sqrt(5x+1)) is

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  15. The solution of the equation intsqrt2^x dx/(xsqrt(x^2-1)=pi/12 is give...

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  16. The value of int(1/e^2)^e abs(logx)dx is

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  17. The integral int0^(pi/2) dx/(x+sqrt(a^2-x^2)) equals

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  18. If I=int0^(pi/4)log(1+tanx) dx then I is equal to

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  19. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

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  20. The value of int0^1 (8log(1+x))/(1+x^2) dx is

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