Home
Class 12
MATHS
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`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    RESONANCE DPP|Exercise All Questions|9 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

Similar Questions

Explore conceptually related problems

If int_(0)^(1)(sin t)/(1+t)dx=alpha, then the value of the integral int_(4 pi-2)^(4 pi)(sin(t)/(2))/(4 pi+2-t)dt is 2 alpha(2)-2 alpha(3)alpha(d)-alpha

If alpha in(-(3 pi)/(2),-pi), then the value of tan^(-1)(cot alpha)-cot^(-1)(tan alpha)+sin^(-1)(sin alpha)+cos^(-1)(cot alpha) is equal to (a)2 pi+alpha(b)pi+alpha(c)0(d)pi-alpha

If m(tan(alpha-theta))/(cos^(2)theta)=n(tan theta)/(cos^(2)(alpha-theta)) the prove that 2 theta=alpha-[tan^(-1)((n-m)/(n+m))tan alpha]

If sin theta =3 sin ( theta + 2 alpha), then the value of tan (theta + alpha) + 2 tan alpha is

If sin theta=3sin(theta+2 alpha), then the value of tan(theta+alpha)+2tan alpha is

If tan(alpha+theta)=n tan(alpha-theta), show that (n+1)sin2 theta=(n-1)sin2 alpha.

If alpha is a root of 25cos^(2)theta+5cos theta-12=0,(pi)/(2)

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

RESONANCE DPP-INTEGRALS-All Questions
  1. int(x^6+1)/(x^2+1)dxi se q u a l (x^5)/5+(x^3)/3+x+c (b) (x^5)/5-(x^...

    Text Solution

    |

  2. If In=intsin^n xdx ; n in N , then 5I4-6I6 is equal to 1.sinx(co...

    Text Solution

    |

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

    Text Solution

    |

  4. int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))= (a) 1/2ln(1+sqrt(1+x^2))+...

    Text Solution

    |

  5. The value of int(-2pi)^(5pi)cot^(-1)(tanx)dxi se q u a lto (7pi)/2 (...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. For Un=int0^1x^n(2-x)^n dx ; Vn=int0^1x^n(1-x)^ndxn in N , which ...

    Text Solution

    |

  10. Evaluate int(x+2)/((x^2+3x+3)sqrt(x+1))dx

    Text Solution

    |

  11. int(cos^3x)/(sqrt(sin^7x))dx= 2/5dotcos e c^(7/2)x+2sqrt(cose c x)+c...

    Text Solution

    |

  12. int0^9{sqrt(x)}dx , where {x} denotes the fractional part of x , is 5 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The value of int1^(e^(37))(pisin(piI nx))/xdx is 2 (b) 4 (c) e^(27)...

    Text Solution

    |

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

    Text Solution

    |

  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...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |