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Chapter 4: Q. 36 (page 404)

Integral Formulas: Fill in the blanks to complete each of the following integration formulas.

鈭�cosxdx=.............

Short Answer

Expert verified

The value of鈭�cosxdx=sinx+C.

Step by step solution

01

Step 1. Given information .

Consider the given function鈭�cosxdx.

02

Step 2. Fill the blank for ∫cos x dx .

The integral of the basic function鈭�cosxdx=sinx+C.

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Most popular questions from this chapter

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2and 鈭�36g(x)dx=3,then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�36fxdx.

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�鈭�32鈥�x2+52xdx

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 heighth1,h2

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The absolute area between the graph of f and the x-axis on [a, b] is equal to|鈭�abf(x)dx|.

(b) True or False: The area of the region between f(x) = x 鈭� 4 and g(x) = -x2on the interval [鈭�3, 3] is negative.

(c) True or False: The signed area between the graph of f on [a, b] is always less than or equal to the absolute area on the same interval.

(d) True or False: The area between any two graphs f and g on an interval [a, b] is given by 鈭�ab(f(x)-g(x))dx.

(e) True or False: The average value of the function f(x) = x2-3 on [2, 6] is

f(6)+f(2)2= 33+12= 17.

(f) True or False: The average value of the function f(x) = x2-3on [2, 6] is f(6)-f(2)4= 33-14= 8.

(g) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 2] and the average value of f on [2, 5].

(h) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 3] and the average value of f on [3, 5].

Suppose f(x)鈮�g(x)on [1, 3] and f(x)鈮�g(x)on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�2, 5] in terms of definite integrals without using absolute values .
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