SOLUTION: find the area under the curve if y=5-x^2

Algebra ->  Pythagorean-theorem -> SOLUTION: find the area under the curve if y=5-x^2      Log On


   

Question 412124: find the area under the curve if y=5-x^2
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28200%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+5+-+x%5E2%29

I'm assuming you want to find the area bounded by the curve and the x-axis...if this is the case, it is simply given by the definite integral

int%285+-+x%5E2%2C+dx%2C+-sqrt%285%29%2C+sqrt%285%29%29 (note that these are the points where the curve meets the x-axis). By the power rule and the First Fundamental Theorem of Calculus, this is equal to 5x+-+x%5E3%2F3 evaluated at sqrt%285%29, minus that expression evaluated at -sqrt%285%29 (Look up "First Fundamental Theorem of Calculus" if you're unsure).