Area Problem

[xomandi]

Find the area of the region bounded by the graph of f(x) = sin(x) - x^3 - x^2 and the x-axis.

So I guess to get area you have to do A = integral sin(x) - x^3 - x^2 dx.
I got A = -cos(x) - 1/4x^4 - 1/3x^3

I am confused on how I get my integrands. Thanks for any help!

 

[galactus]

Graph your function and see where it crosses the x-axis.

Get an idea where it is and you can use Newton's method to hone in on them. This is difficult to solve algebraically.

 

[xomandi]

ack, It's not even clear where they cross. I don't even think we did newton's rule.

 

[galactus]

\(\displaystyle \L\\\int_{-1.463945}^{0}|sin(x)-x^{3}-x^{2}|dx+\int_{0}^{0.59205912}[sin(x)-x^{3}-x^{2}]dx\)