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If int0^1tan^(-1)xdx=alpha,t h e nint0^...

If `int_0^1tan^(-1)xdx=alpha,t h e nint_0^(pi/4)tan^(-1)((2cos^2theta)/(2-sin2theta))sec^2thetadtheta` is equal to: `alpha` (b) `alpha/2` (c) `3alpha` (d) `2alpha`

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RESONANCE DPP ENGLISH-INTEGRALS-All Questions
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  2. If I(n) = int (sin x) ^(n) dx, n in N, then 5I(4) -6I(6) is equal to ...

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  3. If Im=int1^e (lnx)^m dx ,m in N , then I(10)+10 I9 is equal to (A) ...

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  4. int (x dx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))) is equal to

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  5. The value of int(-2pi)^(5pi) cot^(-1)(tan x) dx is equal to

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  6. int((1+(log)e x)^2)/(1+(log)e x^(x+1)+((log)e x^(sqrt(x)))^2)dx=

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  7. intsqrt(1+2cotx(cotx+cos e cx))dx is equal to (A) 2I n(cos x/2)+c (B...

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  8. int0^pisin^3theta(1+2costheta)(1+costheta)^2 d theta is equal to (a...

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  9. If U(n)=int(0)^(1)x^(n)(2-x)^(n)dx and V(n)=int(0)^(1)x^(n)(1-x)^(n)dx...

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  10. int(x+2)/((x^2+3x+3)sqrt(x+1))dx is equal to 1/3tan^(-1)(x/(sqrt(3(x+1...

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  11. int(cos^3x)/(sqrt(sin^7x))dx=

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  12. Evaluate int(0)^(9) {sqrtx} d x , where {x} denotes the fractional par...

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  13. The value of int(-(pi/4)^(1/3))^((pi/4)^(1/3))(x^2)/((1+sin^2x^3)(1+e^...

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  14. If int0^1tan^(-1)xdx=alpha,t h e nint0^(pi/4)tan^(-1)((2cos^2theta)/(...

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  15. If f is a function with period P, then inta^(a+p)f(x)dx is equal to...

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  16. The value of int1^(e^(37))(pisin(piI nx))/xdx is (a) 2 (b) 4 (c) e^...

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  17. int((x^(-7//6)-x^(5//6))dx)/(x^(1//3)(x^(2)+x+1)^(1//2)-x^(1//2)(x^(2)...

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  18. int(-1)^1(x^3|x|+1)/(x^2+2|x|+1)dx=aln2+bt h e n a=2; b=1 (b) a=2; b...

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  19. int((x/e)^x+(e/x)^x)I nxdx= (a)(e/x)^x-(x/e)^x+c (b) (x/e)^x+(e/x...

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  20. Let A=int0^1(e^t)/(t+1)dt , then the value of (int0^1t e^t^2)/(t^2+1)...

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