Finding the values for Integral Notation.

Question

The question says: Express the area of the region under the curve
y = 6x^3 + 5x^2
and above the x-axis as a definite integral.

 

It gives the long s with blanks to the right at the bottom and top- I think this is the A and B value, and a blank to the right of those which is have no idea what that is. I don't understand what it is asking or what to do. Please help me?

Answer 1

You need to first find the lower and upper bounds.  To this this, find the intersection between the function and x-axis.

 

 

Set the function equal to zero.

 

6x³ + 5x² = 0

 

x²(6x + 5) = 0

 

x = 0        and      x = -5/6

 

 

Your lower bound is x=-5/6.

Your upper bound is x=0.

 

So you have

 

⁰_-5/6 ∫(6x³ + 5x²)dx

 

 

Now you can integrate.