The table gives the values of a function obtained from an experiment. Use them to estimate ∫ 3 9 f ( x ) d x using three equal subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. If the function is known to be an increasing function, can you say whether your estimates are less than or greater than the exact value of the integral ? x 3 4 5 6 7 8 9 f ( x ) − 3.4 − 2.1 − 0.6 0.3 0.9 1.4 1.8
The table gives the values of a function obtained from an experiment. Use them to estimate ∫ 3 9 f ( x ) d x using three equal subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. If the function is known to be an increasing function, can you say whether your estimates are less than or greater than the exact value of the integral ? x 3 4 5 6 7 8 9 f ( x ) − 3.4 − 2.1 − 0.6 0.3 0.9 1.4 1.8
Solution Summary: The author explains the theorem (4) to estimate the given integral by using the right endpoints.
The table gives the values of a function obtained from an experiment. Use them to estimate
∫
3
9
f
(
x
)
d
x
using three equal subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. If the function is known to be an increasing function, can you say whether your estimates are less than or greater than the exact value of the integral?
x
3
4
5
6
7
8
9
f
(
x
)
−
3.4
−
2.1
−
0.6
0.3
0.9
1.4
1.8
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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