Again, Last one Find the area of the shaded region

[femmed0ll]

graph 1
http://i38.tinypic.com/290rdib.png

graph 2
http://i36.tinypic.com/dwchp1.png


can you please show the step by step process on how to get the answer(s)? thanks!

 

[HallsofIvy]

For (1) the shaded region lies below the graph of y= x^3+ x^2- 6x and above the graph of y= 6x for x between -4 and 0. Its area is given by
\int_{-4}^0 [(x^3+ x^2- 6x)- 6x]dx

For (2) the shaded region lies below the graph of y= -x^4 and above the graph of y= x^4- 32. Those cross where y= -x^4= x^4- 32 or 2x^4= 32 so that x^4= 16: x= -2 and x= 2. Its area is given by
\int_{-2}^2 [-x^4- (x^4- 32)]dx

 

[Mark44]

Fixed the LaTeX in the first paragraph, some of which wasn't displaying.

For (1) the shaded region lies below the graph of y= x^3+ x^2- 6x and above the graph of y= 6x for x between -4 and 0. Its area is given by
\int_{-4}^0 [(x^3+ x^2- 6x)- 6x]dx

For (2) the shaded region lies below the graph of y= -x^4 and above the graph of y= x^4- 32. Those cross where y= -x^4= x^4- 32 or 2x^4= 32 so that x^4= 16: x= -2 and x= 2. Its area is given by
\int_{-2}^2 [-x^4- (x^4- 32)]dx

 

[HallsofIvy]

Thanks, Mark. I had left out a "/" !

 

[Redbelly98]

That should be more than enough "hints" for the OP to solve the homework problems.

Thread locked, thread moved from "Calculus & Analysis" to Homework & Coursework Questions area.