In Problems 43–54, calculate the definite integral , given that ∫ 1 4 x d x = 7.5 ∫ 1 4 x 2 d x = 21 ∫ 4 5 x 2 d x = 61 3 52. ∫ 5 5 ( 10 − 7 x + x 2 ) d x
In Problems 43–54, calculate the definite integral , given that ∫ 1 4 x d x = 7.5 ∫ 1 4 x 2 d x = 21 ∫ 4 5 x 2 d x = 61 3 52. ∫ 5 5 ( 10 − 7 x + x 2 ) d x
Solution Summary: The author calculates the value of the definite integral displaystyle 'underset' 5overset5int and rewrites it and simplifies.
In Problems 43–54, calculate the definite integral, given that
∫
1
4
x
d
x
=
7.5
∫
1
4
x
2
d
x
=
21
∫
4
5
x
2
d
x
=
61
3
52.
∫
5
5
(
10
−
7
x
+
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.
Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.
90% Confidence interval, to 2 decimals:
( , )
95% Confidence interval, to 2 decimals:
A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.
a. What is the standard error of the mean (to 2 decimals)?
b. At 95% confidence, what is the margin of error (to 2 decimals)?
mean trough level of the population to be 3.7 micrograms/mL. The researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 4.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL. The researcher wants to test at the 5% level of significance if the trough is different than previously reported or not. Z statistics will be used.
Complete Step 5 of hypothesis testing: Conclusion. State whether or not you would reject the null hypothesis and why. Also interpret what this means (i.e. is the mean trough different from 3.7 or no
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY