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Quick Review Once complete, come link calculators!

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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

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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

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Activity Complete the Area under the curve activity.

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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)

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Volume of a sphere Find the volume of a sphere with radius 3 with x=1/2 using RRAM. From -3

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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

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Estimating Area Under the Graph of a Nonnegative Function

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