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Chapter 4: Q. 5 (page 364)
Find a function f that has the given derivative f and value f(c), if possible.
The function f is and the value of (c) is .
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Repeat Exercise 13 for the function f shown above at the right, on the interval
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.
Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
Without calculating any sums or definite integrals, determine the values of the described quantities. (Hint: Sketch graphs first.)
(a) The signed area between the graph of f(x) = cos x and the x-axis on [−π, π].
(b) The average value of f(x) = cos x on [0, 2π].
(c) The area of the region between the graphs of f(x) =
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