In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form ∫ f ( u ) d u . 257. ∫ x 2 x − 1 d x ( x > 1 ) = 2 15 x − 1 ( 3 x 2 + 4 x + 8 ) + C ; u = x − 1
In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form ∫ f ( u ) d u . 257. ∫ x 2 x − 1 d x ( x > 1 ) = 2 15 x − 1 ( 3 x 2 + 4 x + 8 ) + C ; u = x − 1
In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form
∫
f
(
u
)
d
u
.
257.
∫
x
2
x
−
1
d
x
(
x
>
1
)
=
2
15
x
−
1
(
3
x
2
+
4
x
+
8
)
+
C
;
u
=
x
−
1
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.
Female
Male
Totals
Less than High School
Diploma
0.077
0.110
0.187
High School Diploma
0.154
0.201
0.355
Some College/University
0.141
0.129
0.270
College/University Graduate
0.092
0.096
0.188
Totals
0.464
0.536
1.000
Female
Male
Totals
Less than High School
Diploma
0.077
0.110
0.187
High School Diploma
0.154
0.201
0.355
Some College/University
0.141
0.129
0.270
College/University Graduate
0.092
0.096
0.188
Totals
0.464
0.536
1.000
Female
Male
Totals
Less than High School
Diploma
0.077
0.110
0.187
High School Diploma
0.154
0.201
0.355
Some College/University
0.141
0.129
0.270
College/University Graduate
0.092
0.096
0.188
Totals
0.464
0.536
1.000
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY