`int_1^8(x^(-2/3))dx` Evaluate the integral.

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Chapter 5, 5.3 - Problem 24 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Evaluate `int_1^8(x^(-2/3))dx`

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

`=x^(1/3)/(1/3)=3x^(1/3)`

Evaluate the function from x=1 to x=8.

`=3[8^(1/3)-1^(1/3)]`

`=3[2-1]`

=3

 

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