SOLUTION: Find the area between the curves for the equations below and round your answer to one decimal place. y=x^2+9x-4 and y=x+3

Algebra ->  Expressions-with-variables -> SOLUTION: Find the area between the curves for the equations below and round your answer to one decimal place. y=x^2+9x-4 and y=x+3      Log On


   



Question 831664: Find the area between the curves for the equations below and round your answer to one decimal place.
y=x^2+9x-4 and y=x+3

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The curves intersect where x%5E2%2B9x-4=x%2B3
Solving:
x%5E2%2B9x-4=x%2B3
x%5E2%2B9x-4-x-3=0
x%5E2%2B8x-7=0
The solutions are calculated as
x+=+%28-8+%2B-+sqrt%288%5E2-4%2A1%2A%28-7%29+%29%29%2F%282%2A1%29+
x+=+%28-8+%2B-+sqrt%2864%2B28%29%29%2F2+
x+=+%28-8+%2B-+sqrt%2892%29%29%2F2+
x+=+%28-8+%2B-+sqrt%284%2A23%29%29%2F2+
x+=+%28-8+%2B-+2%2Asqrt%2823%29%29%2F2+
x+=-4+%2B-+sqrt%2823%29 (approximately -8.79 and 0.796)
graph%28300%2C300%2C-10%2C5%2C-25%2C5%2Cx%5E2%2B9x-4%2Cx%2B3%29
So the area between the curves can be calculated as

f%28x%29=int%28%28x%5E2%2B8x-7%29%2C+dx%29=x%5E3%2F3%2B4x%5E3-7x so
(rounded)