In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent . 50. ∫ 8 x 7 ( x 8 ) 3 d x
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent . 50. ∫ 8 x 7 ( x 8 ) 3 d x
Solution Summary: The author calculates the value of the indefinite integral by substituting u=x8 with respect to x.
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
50.
∫
8
x
7
(
x
8
)
3
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.
1 2
21. For the matrix A
=
3 4
find AT (the transpose of A).
22. Determine whether the vector
@
1
3
2
is perpendicular to
-6
3
2
23. If v1
=
(2)
3
and v2 =
compute V1 V2 (dot product).
.
7. Find the eigenvalues of the matrix
(69)
8. Determine whether the vector
(£)
23
is in the span of the vectors
-0-0
and
2
2
1. Solve for x:
2. Simplify:
2x+5=15.
(x+3)² − (x − 2)².
-
b
3. If a = 3 and 6 = 4, find (a + b)² − (a² + b²).
4. Solve for x in 3x² - 12 = 0.
-
Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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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