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Evaluate the following : int(4)^(7)((...

Evaluate the following :
`int_(4)^(7)((11-x)^(3))/(x^(3)+(11-x)^(3))dx`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_{4}^{7} \frac{(11-x)^{3}}{x^{3} + (11-x)^{3}} \, dx, \] we can use a property of definite integrals. Specifically, we can exploit the symmetry of the integral by substituting \( x \) with \( 11 - x \). ...
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Knowledge Check

  • int_(4)^(7)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=

    A
    `(1)/(2)`
    B
    1
    C
    `(3)/(2)`
    D
    2

  • int_(0)^(11)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=

    A
    2
    B
    `11/2`
    C
    `4`
    D
    `1/2`

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