Think About It The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. (a) ∫ 0 2 f ( x ) d x (b) ∫ 2 6 f ( x ) d x (c) ∫ − 4 2 f ( x ) d x (d) ∫ − 4 6 f ( x ) d x (e) ∫ − 4 6 | f ( x ) | d x (f) ∫ − 4 6 [ f ( x ) + 2 ] d x
Think About It The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. (a) ∫ 0 2 f ( x ) d x (b) ∫ 2 6 f ( x ) d x (c) ∫ − 4 2 f ( x ) d x (d) ∫ − 4 6 f ( x ) d x (e) ∫ − 4 6 | f ( x ) | d x (f) ∫ − 4 6 [ f ( x ) + 2 ] d x
Solution Summary: The author explains how to calculate the integral displaystyleint_02f(x)dx.
Think About It The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas.
(a)
∫
0
2
f
(
x
)
d
x
(b)
∫
2
6
f
(
x
)
d
x
(c)
∫
−
4
2
f
(
x
)
d
x
(d)
∫
−
4
6
f
(
x
)
d
x
(e)
∫
−
4
6
|
f
(
x
)
|
d
x
(f)
∫
−
4
6
[
f
(
x
)
+
2
]
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Consider the function f(x) = /x+1-
9 for the domain -1, o0).
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1
Find f(x), wheref is the inverse of f.
-1
Also state the domain of f in interval notation.
(x) = for the domain
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DVO (0,0) [0,0)
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Explanation
Check
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Determine where F(x) is positive and where it is negative. Write your answer in interval notation.
Calculus one
Which is a correct formula for finding the derivative of the product of two functions a and b?
O (ab)'= a'b'
(ab)' = a'b + ab'
(ab)'= a'+b'
Use the correct formula above to find the derivative of the function f(x) = (x³ + 5)√x.
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