Consider the following. 81 - x2, [0, 9] (a) Sketch the graph of the function, highlighting the part indicated by the given interval. 80 80 60 60 У 40 y 40 20 20 -10 -8 -6-4 -2 0 2 8 10 -10 8 -6 -4 -2 0 2 4 8/ 10 4 6 -20 -20 -40 40 -60 -60 -80 -80 80 60 60 y 40 y 40 20 20 -10-8 -6 -4 -2 . 2 6 8 10 0. -10 8 -6 -4 -2 2 4 6 8/ 10 -20 -20 -40 -40 -60 -60 -80 (b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far. 9 dx
Consider the following. 81 - x2, [0, 9] (a) Sketch the graph of the function, highlighting the part indicated by the given interval. 80 80 60 60 У 40 y 40 20 20 -10 -8 -6-4 -2 0 2 8 10 -10 8 -6 -4 -2 0 2 4 8/ 10 4 6 -20 -20 -40 40 -60 -60 -80 -80 80 60 60 y 40 y 40 20 20 -10-8 -6 -4 -2 . 2 6 8 10 0. -10 8 -6 -4 -2 2 4 6 8/ 10 -20 -20 -40 -40 -60 -60 -80 (b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far. 9 dx
Consider the following. 81 - x2, [0, 9] (a) Sketch the graph of the function, highlighting the part indicated by the given interval. 80 80 60 60 У 40 y 40 20 20 -10 -8 -6-4 -2 0 2 8 10 -10 8 -6 -4 -2 0 2 4 8/ 10 4 6 -20 -20 -40 40 -60 -60 -80 -80 80 60 60 y 40 y 40 20 20 -10-8 -6 -4 -2 . 2 6 8 10 0. -10 8 -6 -4 -2 2 4 6 8/ 10 -20 -20 -40 -40 -60 -60 -80 (b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far. 9 dx
(b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far.
(c) Use the integration capabilities of a graphing utility to approximate the arc length. (Round your answer to three decimal places.)
Transcribed Image Text:Consider the following.
81 – x2, [0, 9]
(a) Sketch the graph of the function, highlighting the part indicated by the given interval.
80
80
60
60
у 40
У 40
20
-10 -8 -6 -4 -2 0
4
8 10
-10 -8 -6
-4 -2
2
4
6.
8
10
-20
-20
-40
-40
-60
-60
-80
80
80
60
60
У 40
y 40
20
20
-10 -8 -6 -4
-2
2
6 8 10
4
-10 8 -6 -4 -2
2
4
6
8/ 10
-20
-20
-40
-40
-60
-60
-80
(b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far.
9.
dx
20
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.
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![Consider the following.
81 – x2, [0, 9]
(a) Sketch the graph of the function, highlighting the part indicated by the given interval.
80
80
60
60
у 40
У 40
20
-10 -8 -6 -4 -2 0
4
8 10
-10 -8 -6
-4 -2
2
4
6.
8
10
-20
-20
-40
-40
-60
-60
-80
80
80
60
60
У 40
y 40
20
20
-10 -8 -6 -4
-2
2
6 8 10
4
-10 8 -6 -4 -2
2
4
6
8/ 10
-20
-20
-40
-40
-60
-60
-80
(b) Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far.
9.
dx
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf2a9245-87db-4e54-b147-768ccba693e7%2F404f6583-ae34-4871-b23e-959372603f60%2Fmhtq81aw_processed.jpeg&w=3840&q=75)
