Home
Class 12
MATHS
Prove that int(0)^(2a)f(x)dx=int(0)^(a)[...

Prove that `int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx`

Text Solution

AI Generated Solution

To prove the equation \[ \int_{0}^{2a} f(x) \, dx = \int_{0}^{a} [f(a-x) + f(a+x)] \, dx, \] we will start from the right-hand side (RHS) and manipulate it to show that it equals the left-hand side (LHS). ...
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(a)f(x)dx

Prove that: int_0^(2a)f(x)dx=int_0^(2a)f(2a-x)dxdot

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

int_(m)^(0)f(x)dx is

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx

Prove that int_-2^2 f(x^4)dx=2int_0^2 f(x^4)dx

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx is equal to

CENGAGE ENGLISH-DEFINITE INTEGRATION -JEE ADVANCED
  1. Prove that int(0)^(2a)f(x)dx=int(0)^(a)[f(a-x)+f(a+x)]dx

    Text Solution

    |

  2. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

    Text Solution

    |

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

    Text Solution

    |

  5. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

    Text Solution

    |

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

    Text Solution

    |

  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

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

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  15. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

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

    Text Solution

    |

  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. find the period of sin(x/2)-cos(x/3) is

    Text Solution

    |

  21. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

    Text Solution

    |