CPM Homework Help : CALC Problem 4-109

Find the area of the region in the second quadrant under the function $y = x^3 + 2x^2-3x$ .

Hint:

To set up the integral, first determine the bounds in which this function exists in the 2nd quadrant.

Step 1:

Determine the roots:
$0 = x^3 + 2x^2 − 3x$
$0 = x(x^2 + 2x − 3) = x(x + 3)(x − 1)$
Roots: $x = 0$ , $x = −3$ , and $x = 1$
2nd quadrant domain: $[-3, 0]$

Step 2:

Integrate.

Answer:

$\int_{-3}^0(x^3+2x^2-3x)dx=$