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 . 49. ∫ 5 x 4 ( x 5 ) 4 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 . 49. ∫ 5 x 4 ( x 5 ) 4 d x
Solution Summary: The author explains how to calculate the value of the indefinite integral without using substitution method.
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.
49.
∫
5
x
4
(
x
5
)
4
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.
Problem 4. Let
f(x, y) =
{
Find P(X <1/2|Y = 1/2).
c(x + y²) 0
Qize
f(x)
x + 2x2 - 2
x² + 4x² - 4
Solve the equation using Newton
Raphson
3. Consider the following theorem:
Theorem: If n is an odd integer, then n³ is an odd integer.
Note: There is an implicit universal quantifier for this theorem. Technically we could write:
For all integers n, if n is an odd integer, then n³ is an odd integer.
(a) Explore the statement by constructing at least three examples that satisfy the hypothesis,
one of which uses a negative value. Verify the conclusion is true for each example. You
do not need to write your examples formally, but your work should be easy to follow.
(b) Pick one of your examples from part (a) and complete the following sentence frame:
One example that verifies the theorem is when n =
We see the hypothesis is
true because
and the conclusion is true because
(c) Use the definition of odd to construct a know-show table that outlines the proof of the
theorem. You do not need to write a proof at this time.
Chapter 5 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
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