1. Quick Review Once complete, come link calculators!

3. Definite Integrals and Area under the curve Find the area under the curve below. If a=4 and b=8. Find a formula. What could you do to find the area under this curve? ab f(x)=8 a=0b

4. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x=0 to x=3 Using Rectangular Approximation Method to find area under the curve Left RAM or LRAM Midpoint RAM or MRAM Right RAM or RRAM

5. Activity Complete the Area under the curve activity.

6. Formulas needed Write the formulas for; Distance/rate/time Trapezoid Area Circle/half Circle Volume of a Cylinder Answers D=rt A=1/2h(b 1 +b 2 ) y=r 2 -x 2 (Equation for circle, rotated is a sphere) V=πr 2 h (rotated around rectangles become cylinders) Put them together. (y in for r)

7. Volume of a sphere Find the volume of a sphere with radius 3 with x=1/2 using RRAM. From -3<x<3 From 1<x<3 Rotate the Rectangle. What shape does it make? How do you find the volume of that shape? How does that work with the equation of the sphere?

8. Finding Distance Traveled when Velocity Varies The area under the curve approximates the total distance traveled. Use t=.25 to approximate from t=0 to t=3

9. Estimating Area Under the Graph of a Nonnegative Function