### Home > CALC > Chapter 4 > Lesson 4.3.2 > Problem 4-109

4-109.

Find the area of the region in the second quadrant under the function *y *=* x*^{3} + 2*x*^{2 }− 3*x*. Homework Help ✎

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

Determine the roots:

0 = *x*^{3} + 2*x*^{2} − 3*x*

0 = *x*(*x*^{2} + 2*x* − 3) = *x*(*x* + 3)(*x* − 1)

Roots: *x* = 0, *x* = −3, and *x* = 1

2nd quadrant domain: [−3, 0]

Integrate.