Home
Class 12
MATHS
Let p(x) be a function defined on R such...

Let p(x) be a function defined on R such that `p'(x) = p'(1-x)`, for all `x in [0,1],p(0) = 1` and `p(1) = 41`. Then show that `int_(0)^(1) p(x) dx = 21`

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise - 2.7 (Level-2)|21 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in [0, 1], P(0)=1, P(1) =41 then int_(0)^(1)P(x)dx=

Let f: R to R be a function such that for some p gt 0 , f(x+p) = (f(x)- 5)/( f(x) - 3) for all x in R . Then period of f is

p(x) = x^(2)-x+k, p(1) = -1 then k = …………

Let X be a random varibale such that P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = (1)/(6) and P(X = 0) = (1)/(3) .

If p(x) is a polynomial such that p(x^2+1)={p(x)}^2+1 and p(0)=0 then p^1(0) is equal to

Let X be a random variable such that P(X = - 2) = P ( X = - 1) = P ( X = 2) = P ( X = 1) = 1//6 and P (X = 0 ) = 1//3 , then find the mean of x .

If X is a Poisson distribution such that P(X=0)=P(X=1) , then P(X=3)=

p(x) = 2x+1 then p(-1//2) =

AAKASH SERIES-DEFINITE INTEGRALS-Exercise (Level-2)
  1. Show that int(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3...

    Text Solution

    |

  2. Show that int(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5)...

    Text Solution

    |

  3. Show that int(0)^(pi//2)(sin x cos x)/(cos^(2) x + 3 cos x + 2)dx = lo...

    Text Solution

    |

  4. Show that int(0)^(1//3)(dx)/((1+x^(2))sqrt(1-x^(2))) = (pi)/(4sqrt(2))

    Text Solution

    |

  5. Show that int(0)^(1)(dx)/((1+x^(2))sqrt(2+x^(2))) = (pi)/(6)

    Text Solution

    |

  6. Show that int(0)^(1//2) (dx)/((1-2x^(2))sqrt(1-x^(2))) = (1)/(2) log(2...

    Text Solution

    |

  7. int(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=

    Text Solution

    |

  8. Show that int(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2)...

    Text Solution

    |

  9. Show that int(0)^(pi//4) sqrt(tan theta) d theta = (1)/(sqrt(2)) log(s...

    Text Solution

    |

  10. Show that int(0)^(pi//4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4)x...

    Text Solution

    |

  11. Show that int(0)^(pi//2)(sinxcos x)/(1+sin^(4)x)dx = (pi)/(8)

    Text Solution

    |

  12. Prove that int(0)^(pi//2)(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx = (sqr...

    Text Solution

    |

  13. Show that int(0)^(oo) (dx)/((x+sqrt(1+x^(2)))^(n))=(n)/(n^(2)-1), (n i...

    Text Solution

    |

  14. int(0)^(pi//4)[sqrt(tan x) + sqrt(cot x)] = dx

    Text Solution

    |

  15. Show that int(0)^(pi//2)(sqrt(tan x)+sqrt(cot x))dx = pisqrt(2)

    Text Solution

    |

  16. Find the value of Lim(x rarr 0) (1)/(x^(3)) int(0)^(x) (t(ln (1+t)))/...

    Text Solution

    |

  17. Find the value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx

    Text Solution

    |

  18. For any real number x, let [x] denote the largest less than or equal t...

    Text Solution

    |

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

    Text Solution

    |

  20. Let p(x) be a function defined on R such that p'(x) = p'(1-x), for all...

    Text Solution

    |