1. APPLICATIONS OF INTEGRATION AREA BETWEEN 2 CURVES

2. We want to find the area between f(x) = x 2 and g(x) = -x + 6. Always graph the two functions first to get a visual of the area.

3. FIND POINTS OF INTERSECTION Because we only want the area between, we have to find the points of intersection. To do this, set f(x) = g(x) and solve for x. x 2 = -x + 6 x = -3 and 2

4. FIND THE AREA UNDER BOTH CURVES

5. FORMULA left point of intersection right point of intersection upper function lower function

6. PRACTICE Set up and solve the integral to find the area between f(x) = 2 – x 2 and g(x) = -x. Area is 9/2 units squared

7. TO USE THE CALCULATOR Input the two equations into y1 and y2. Graph and find the two intersections.  2 nd CALC  intersect  ENTER  “First curve?” ENTER  “Second curve?” ENTER  “Guess?” Move cursor over one intersection point, ENTER  Get solution, repeat steps for second intersection point x = -1 and 2

8. TO USE THE CALCULATOR

9. YOUR TURN! Fill in the blanks for each problem. 1. Graph 2. Intersection points: x = _________ 3. Upper function: _______________ Lower function: _______________ 4. Integral: _____________________ 5. Area: ________________________

10. PROBLEMS 1.Find the area of the region enclosed by f(x) = 2 cos x and g(x) = x 2 – 1 A = 4.99 un 2 2.Find the area of the region enclosed by f(x) = 7 – 2x 2 and g(x) = x 2 + 4 A = 4 un 2

11. ASSIGNMENT page 4521 – 6, 20 – 55 by 5