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Property 6: If f(x) is a continuous func...

Property 6: If f(x) is a continuous function defined on `[0, 2a]` then ` int_0 ^(2a)f(x)dx = int_0 ^a f(x) dx + int_0 ^a f(2a - x) dx`

Answer

Step by step text solution for Property 6: If f(x) is a continuous function defined on [0, 2a] then int_0 ^(2a)f(x)dx = int_0 ^a f(x) dx + int_0 ^a f(2a - x) dx by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Property 5: If f(x) is a continuous function defined on [0;a] then int_(0)^(a)f(x)dx=int_(0)f(a-x)dx

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Knowledge Check

  • int_0^a f(a-x) dx=

    A
    `int_0^(2a) f(x) dx`
    B
    `int_(-a)^a f(x) dx`
    C
    `int_0^a f(x) dx`
    D
    `int_a^0 f(x) dx`.

  • If int_(0)^(2a) f(x)dx=int_(0)^(2a) f(x)dx , then

    A
    `f(2a-x)=-f(x)`
    B
    `f(2a-x)=f(x)`
    C
    f(x) is an odd function
    D
    f (x) is an even function

  • If : int_(0)^(2a)f(x)dx=2.int_(0)^(a)f(x)dx , then :

    A
    `f(2a-x)=-f(x)`
    B
    `f(2a-x)=f(x)`
    C
    `f(a-x)=-f(x)`
    D
    `f(a-x)=f(x)`

    • Similar Questions

    Explore conceptually related problems

    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

    Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

    Property 10: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=2int_(0)^(a)f(x)dx if f(2a-x)=f(x) and 0 if f(2a-x)=-f(x)

    prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

    Property 7: Let f(x) be a continuous function of x defined on [0;a] such that f(a-x)=f(x) then int_(0)^(a)xf(x)dx=(a)/(2)int_(0)^(a)f(x)dx

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