Home
Class 12
MATHS
If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1)...

If `f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):}` and `g(x)=f(x-1)+f(x+1),` then find the value of `int_(-3)^5g(x)dx`.

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-)+f(x + 1) , for all x in R .Then,the value of int_-3^3 g(x)dx is

If f:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(x))dx

If f(x)=min{|x-1|,|x|,|x+1|, then the value of int_-1^1 f(x)dx is equal to

If f(x) = (1)/(1 -x) x ne 1 and g(x) = (x-1)/(x) , x ne0 , then the value of g[f(x)] is :

If f(x)=|x-2|+x^(2)-1 and g(x)+f(x)=x^(2)+3 , find the maximum value of g(x) .

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(1) is

If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt 0):}

If for non zero x , 3f(x)+4f((1)/(x))=(1)/(x)-10 , then the value of int_(2)^(3)f(x)dx is

Let f(x) be a function satisying f(x) = f((100)/(x)) AA x ge 0 . If int_(1)^(10) (f(x))/(x) dx = 5 then find the value of int_(1)^(100)(f(x))/(x) dx .

If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x) , then the value of g ′ (1) is

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Determine a positive integer nlt=5 such that int0^1e^x(x-1)^n=16-6e

    Text Solution

    |

  2. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |

  3. If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), th...

    Text Solution

    |

  4. Evaluate: int0^(1)sin^(-1)((2x)/(1+x^2))dx

    Text Solution

    |

  5. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

    Text Solution

    |

  6. L e t \ f(n)=1+1/2+1/3+...+1/n. Then show that f(n)=int0^(pi/2)cot(the...

    Text Solution

    |

  7. Let f(x) be a continuous function AAx in R , except at x=0, such that...

    Text Solution

    |

  8. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

    Text Solution

    |

  9. Determine a positive integer n such that int0^(pi/2)x^nsinx dx=3/4(pi^...

    Text Solution

    |

  10. f,g,h are continuous in [0,1],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...

    Text Solution

    |

  11. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

    Text Solution

    |

  12. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

    Text Solution

    |

  13. Evaluate: int3^10[log[x]]dx

    Text Solution

    |

  14. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |

  15. The value of int0^1(x^4(1-x)^4)/(1+x^2)dx is/are (a)(22)/7-pi (b)...

    Text Solution

    |

  16. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

    Text Solution

    |

  17. Evaluate:int-pi^pi ((2x)(1+sinx)/(1+cos^2x))dx

    Text Solution

    |

  18. Q. if int0^100(f(x) dx = a, then sum(r=1)^100(int0^1( f(r-1+x)dx))=

    Text Solution

    |

  19. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

    Text Solution

    |

  20. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

    Text Solution

    |