 # Lab 5.1 and 5.2 1. Estimate the area under f(x) using the picture ...

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Lab 5.1 and 5.2 1. Estimate the area under f(x) using the picture below. 2. Estimate the area under f(x) = x 2 + 2 on the interval [−2, 0] using lower sums and two rectangles, and on the interval [0, 3] using upper sums and three rectangles. Combine these together to find the area under f(x) 3. Estimate the area under f(x) = x 2+2 on the interval [−2, 3] using upper sums and five rectangles. 4. Estimate the area under f(x) = x 2 + 2 on the interval [−2, 3] using midpoint sums and five rectangles. 5. Estimate the area under f(x) = x 2 + 2 on the interval [−2, 3] using lower sums and five rectangles. 6. Write a summation approximating the area under f(x) = x 2 on the interval [−1, 1] with n rectangles using right endpoints. 7. Write a summation approximating the area under f(x) = x 2 on the interval [−1, 1] with n rectangles using left endpoints. 8. Write a summation approximating the area under f(x) = x 3 on the interval [−1, 1] with n rectangles using right end points. 9. Plug n = 4 into the answer to the previous question. Does this answer make sense? Why or why not? 10. For the following functions find a formula for the Riemann Sum obtained by dividing the interval [a,b] into n equal subintervals and using the right and endpoint for each, then take the limit as n approaches infinity to calculate the area under the curve. (a) f(x) = 1 − x 2 over the interval [0, 1] Continued from previous page (b) f(x) = x 2 + 1 over the interval [0, 3] (c) f(x) = 3x + 2x 2 over the interval [0, 1

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