(a)
To find: The integral.
(a)
Answer to Problem 42E
The integral is:
Explanation of Solution
Given information:
The
Calculation:
Put
Use integration by parts
Let,
Then,
Evaluate the remaining integral after rewriting it using integration by parts.
The required integral of the given integration
(b)
To find: The integral.
(b)
Answer to Problem 42E
The integral is:
Explanation of Solution
Given information:
The integration is
Calculation:
Put
Use integration by parts
Let,
Then,
Evaluate the remaining integral after rewriting it using integration by parts.
From part (a)
The required integral of the given integration
(c)
To find: The integral.
(c)
Answer to Problem 42E
The integral is:
Explanation of Solution
Given information:
The integration is
Calculation:
Put
Use integration by parts
Let,
Then,
Evaluate the remaining integral after rewriting it using integration by parts.
From part (b)
The required integral of the given integration
(d)
To find: The value of the integral for any positive integer of
(d)
Answer to Problem 42E
The integral is:
Explanation of Solution
Given information:
The integration is
Calculation:
When
When
When
The outcomes were of the form
Each polynomial's terms contain alternating signs that begin with +. Aside from the + or -, each phrase is also the derivative of the one before it.
The polynomials are then of the form
The integral's outcome can then be expressed in write as:
Therefore the required value of the integral for any positive integer of
(e)
To check: The convincing argument that conjecture in part (d) is true or false,
(e)
Answer to Problem 42E
The option (d) is true.
Explanation of Solution
Given information:
The integration is
Calculation:
From part d)
Use tubular integration
Then gives,
To use the operation signs above each arrow, combine the results of the functions connected by the arrows to produce:
The last term has a sign of
Therefore, the required conjecture from part d) is true.
Chapter 6 Solutions
CALCULUS-W/XL ACCESS
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