Home
Class 12
MATHS
For any real number, let [x] denotes the...

For any real number, let `[x]` denotes the largest integer less than or equal to `x`. Let f be a real valued function defined on the interval `[-10,10]` by
`f(x)= {{:(x-[x]" ""if"" "[x] "" "is odd"),(1+[x]-x" ""if"" "[x]"is even"):}`
Then the value of `(pi^(2))/(-10) int_(10)^(10) f(x) cos pix dx` is

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

For any real number x ,l e t[x] denote the largest integer less than or equal to x ,L e tf be a real-valued function defined on the interval [-10 , 10] be f(x)={x-[x],if[x]i sod d1+[x]-x ,if[x]i se v e n Then the value of (pi^2)/(10)int_(-1)^(10)f(x)cospixdxi s____

For any real number x, let [x] = largest integer less than or equalto x. Let f be a real valued function defined on the interval [-10,10] by Then, the value of (pi/10)^2 (int_-10^10 f(x) cos pi x dx is

For any real number x, Let [x] denote the largest integer less than or equal to x. The value of 9 int_0^9 [sqrt frac{10x}{x 1}] dx

For a real number x let [x] denote the largest number less than or equal to x. For x in R let f (x)=[x] sin pix . Then

For any real number x, let [x] denote the largest integer less than or equal to x. If int_0^10 [sqrt((10x)/(x+1))]dx then the value of 9I is

For a real number x, let [x] denote the greatest integer less than or equal to x. Let R rarr R be defined as f(x)=2x+[x]+sin x cos x then f is

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. The value(s) of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2))dx is are

    Text Solution

    |

  2. Let f be a real-valued function defined on the interval (0,oo) by f(x)...

    Text Solution

    |

  3. For any real number, let [x] denotes the largest integer less than or ...

    Text Solution

    |

  4. Let f be a real-valued function defined on the interval (-1,1) such th...

    Text Solution

    |

  5. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  6. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  7. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  8. The value of int(sqrt(ln2))^(ln3)(xsinx^(2))/(sinx^(2)+sin(ln6-x^(2)))...

    Text Solution

    |

  9. Let the straight line x = b divide the area enclosed by y = (1-x)^(2),...

    Text Solution

    |

  10. Let f : [-1,2]rarr[0,oo) be a continuous function such that f(x) = f(1...

    Text Solution

    |

  11. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  12. The value of the integral int(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) ...

    Text Solution

    |

  13. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  14. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  15. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

    Text Solution

    |

  16. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |

  17. Let f : [1/2, 1] rarr R (the set of the all real numbers) be a positiv...

    Text Solution

    |

  18. For a in R (the set of all real numbers), a ne = - 1, lim(nrarroo)((...

    Text Solution

    |

  19. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  20. Let f : (0,oo) rArr R be given f(x) = underset(1/x)overset(x)e^((1+(dt...

    Text Solution

    |