Let ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a5_f8b3_9f8f_d3756c7e286e_TB5971_11.jpg)
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a.Use Part 1 of the Fundamental Theorem of Calculus to find ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_1fc4_9f8f_139ea51780a1_TB5971_11.jpg)
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b.Use Part 2 of the Fundamental Theorem of Calculus to integrate ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_1fc5_9f8f_035219f062fe_TB5971_11.jpg)
to obtain an alternative expression for F(x).
c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1
If f is continuous on [a, b], then the function F defined by ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_46d6_9f8f_4f4da712b2a5_TB5971_11.jpg)
is differentiable on (a, b), and ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_46d7_9f8f_c3bc40309522_TB5971_11.jpg)
The Fundamental Theorem of Calculus, Part 2
If f is continuous on [a, b], then ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_46d8_9f8f_91f5f7a42169_TB5971_11.jpg)
where F is any antiderivative of f, that is, ![Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, .](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_55a6_6de9_9f8f_cf10a69dd2cf_TB5971_11.jpg)
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Definitions:
Null Hypothesis
A hypothesis that assumes no statistical significance exists in a set of given observations.
Sample Mean
The arithmetic average of a set of sample values, used as an estimate of the population mean.
Null Hypothesis
A statement or assumption that there is no significant difference or effect, serving as the default conclusion until evidence suggests otherwise.
Critical Value
A threshold in statistical hypothesis testing that defines the boundary or limit beyond which an observed test statistic is considered statistically significant.
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