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anonymous

  • 4 years ago

Calculus question. Why is ∫85−3(√25−t)dt equal to 2(25−t)3/2+85t and not 85t−2(25−t)3/2

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  1. anonymous
    • 4 years ago
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    *Rewriting to use TeX* \[\int\limits_{}^{}(85 - 3\sqrt(25-t))dt\] equal to \[2(25-t)^{3/2}+85t\] and not \[85t - 2(25-t)^{3/2}\] Why?

  2. Mr.Math
    • 4 years ago
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    Use a substitution \(u=25-t\) and see what you get.

  3. phi
    • 4 years ago
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    or take the derivative of each of your answers. Only one will give the correct result.

  4. Mr.Math
    • 4 years ago
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    I see where you went wrong. You replaced \(dt\) by \(du\) and this is wrong, because \(u=25-t \implies du=-dt\). Makes sense?

  5. anonymous
    • 4 years ago
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    How does u = (25-t) imply that du = -dt?

  6. Mr.Math
    • 4 years ago
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    If u=25-t, what's du/dt?

  7. Mr.Math
    • 4 years ago
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    The derivative of u with respect to t is obviously \(\frac{du}{dt}=-1\). Multiply both sides by \(dt\) you get \(du=-dt\).

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