User:Xhuwin
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THANK YOU, SHERWIN ~nona
1. Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 3 using four approximating rectangles and right endpoints. Round answer to the nearest whole number.
2. Use the Midpoint Rule with the given value of n to approximate the integral: n = 5. Round answer to the nearest whole number.
3. Use the definition of a definite integral to evaluate the integral (form: .
4. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Then evaluate the derivative when x = 2.
5. Evaluate the integral: . Round answer to the nearest whole number.
6. Evaluate the integral: . Round answer to the nearest hundredths.
7. Evaluate the integral: .
8. Evaluate the integral: .
* 1 recipe pastry for a 9 inch double crust pie * 4 tablespoons quick-cooking tapioca * 1/8 teaspoon salt * 1 cup white sugar * 4 cups pitted cherries * 1/4 teaspoon almond extract * 1/2 teaspoon vanilla extract * 1 1/6 tablespoons butter
Solutions:
1. The width of each rectangle is ½. The endpoints are at f (1.5), f (2), f (2.5), f (3). A = ½*[ f (1.5) + f (2) + f (2.5) + f (3)] = 0.95 = 1 (rounded) = 1 9-inch pie crust
2. The width of each rectangle is 1. The midpoints are at f (.5), f (1.5), f (2.5), f (3.5), f (4.5). A = 1*[ f (.5) + f (1.5) + f (2.5) + f (3.5) + f (4.5)] = 4.3978 = 4 (rounded) = 4 tablespoons quick-cooking tapioca
3.
= 10 + 0 − 27 / 3 + 0 + 0
= 1 cup of white sugar
4. 1/8 teaspoon salt
5.
4 cups pitted cherries
6. teaspoon almond extract
7. teaspoon vanilla extract
8. tablespoons butter