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If I(n)=underset(0)overset(pi//4)inttan^...

If `I_(n)=underset(0)overset(pi//4)inttan^(n)x dx`, then
`(1)/(I_(2)+I_(4)),(1)/(I_(3)+I_(5)),(1)/(I_(4)+I_(6)),...` from

A

A.P.

B

G.P.

C

H.P.

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  2. Let I (1) = int (1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I (2) = int (1) ...

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  3. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  4. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

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  5. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

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  6. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  7. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

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  8. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  9. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

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  10. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  11. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

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  12. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  13. underset(2-ln3)overset(3+ln3)int(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal...

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  14. If [x] stands for the greatest integer function, the value of overset(...

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  15. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

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  16. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

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  17. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  18. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  19. lim( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......

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  20. The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(...

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