Home
Class 12
MATHS
Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x...

Let `f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x` for all `x in (-pi/2,pi/2)` . Then the correct expression (s) is (are) (a) `int_0^(pi/4)xf(x)dx=1/(12)` (b) `int_0^(pi/4)f(x)dx=0` (c) `int_0^(pi/4)xf(x)=1/6` (d) `int_0^(pi/4)f(x)dx=1/(12)`

A

`underset(0)overset(pi//4)intxf(x) dx = 1/12`

B

`underset(0)overset(pi//4)intf(x) dx = 0`

C

`underset(0)overset(pi//4)intxf(x) dx = 1/6`

D

`underset(0)overset(pi//4)intf(x) dx = 1`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

int_0^(pi/2)1/(1+tan^2x)dx

int_0^1(tan^(-1)x)/x dx is equals to (a) int_0^(pi/2)(sinx)/x dx (b) int_0^(pi/2)x/(sinx)dx (c) 1/2int_0^(pi/2)(sinx)/x dx (d) 1/2int_0^(pi/2)(""x)/(sinx)dx

int_0^(pi/4) (tanx-x)tan^2xdx

Evaluate: int_0^(pi//4)sqrt(1+sin2x)dx (ii) int_0^(pi//4)sqrt(1-sin2x)dx

Prove that int_(0)^(tan^(-1)x)/x dx=1/2int_(0)^((pi)/2)x/(sinx)dx .

Let 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)).cos x dx , then :

Evaluate: int_0^(pi//4)tan^2x dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

Evaluate: int_0^(pi//4)tan^2x\ dx

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  2. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  3. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  4. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  5. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

    Text Solution

    |

  10. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  11. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

    Text Solution

    |

  12. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

    Text Solution

    |

  13. Let f:Rto(0,1) be a continuous function. Then, which of the following ...

    Text Solution

    |

  14. Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...

    Text Solution

    |

  15. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...

    Text Solution

    |

  16. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

    Text Solution

    |

  17. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(...

    Text Solution

    |

  18. For each positive integer n let y(n)=1/n((n+1)(n+2)…..(n+n)^(1//n))....

    Text Solution

    |

  19. A farmer F(1) has a land in the shape of a triangle with vertices at P...

    Text Solution

    |

  20. The value of the integral int(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^(6...

    Text Solution

    |