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Chapter 4: Q. 2 (page 404)
Calculating sums: Determine the value of each of the sums that
follow. Some can be computed directly, some require the use
of sum formulas, and for some you will have to also compute
a limit .
The value is.
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Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.
Given a simple proof that
Given a simple proof that if n is a positive integer and c is any real number, then
Given formula for the areas of each of the following geometric figures
a) area of circle with radius r
b) a semicircle of radius r
c) a right triangle with legs of lengths a and b
d) a triangle with base b and altitude h
e) a rectangle with sides of lengths w and l
f) a trapezoid with width w and height
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
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