`int_-1^2(x^3 - 2x)dx` Evaluate the integral.

Textbook Question

Chapter 5, 5.3 - Problem 19 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the integral, such that:

`int_(-1)^2(x^3 - 2x)dx = int_(-1)^2 x^3 dx - int_(-1)^2 2x dx`

`int_(-1)^2(x^3 - 2x)dx = (x^4/4 - x^2)|_(-1)^2`

`int_(-1)^2(x^3 - 2x)dx = (2^4/4 - 2*2 - (-1)^4/4 - 2)`

`int_(-1)^2(x^3 - 2x)dx = 4 - 4 -1/4 - 2`

`int_(-1)^2(x^3 - 2x)dx = -9/4`

Hence evauating the definite integral yields `int_(-1)^2(x^3 - 2x)dx = -9/4.`

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