`int_0^4(4 - t)(sqrt(t))dt` Evaluate the integral.

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Chapter 5, 5.3 - Problem 28 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Evaluate `int_0^4(4-t)(sqrt(t))dt`

`=int_0^4(4t^(1/2)-t^(3/2))dt`

Integrate the function.   `inta^n=a^(n+1)/(n+1)`

`=(4t^(3/2))/(3/2)-t^(5/2)/(5/2)=(8/3)t^(3/2)-(2/5)t^(5/2)`

Evaluate the function from t=0 to t=4.

`=[(8/3)(4)^(3/2)-(2/5)(4)^(5/2)]-[(8/3)(0)^(3/2)-(2/5)(0)^(5/2)]`

=8.533

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