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If f is a continuous function on [a, b] ...

If f is a continuous function on `[a, b]` and `u(x)` and `v(x)` are differentiable functions of x whose values lie in `[a, b]` then `d/dx { int_(u(x)) ^(v(x)) f(t) dt} = f(v(x)) d(v(x))/dx - f(u(x)) d(u(x))/dx`

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Knowledge Check

  • Find d/(dx)(int_(x^2)^(x^3) 1/(logt) dt) .

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    B
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    A
    f(c) where `c in (0,2)`
    B
    `2f(c),` where `c in (0, 2)`
    C
    `f'(c)` where `c in (0, 2)`
    D
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    A
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    D
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