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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.6, Problem 1CP
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

True or false: In evaluating ∫ u   d v by parts,

(a) the parts u and dv are selected and the parts du and v are calculated.

(b) the differential (often dx) is always chosen as part of dv.

(c) the parts du and v are found from u and dv as follows:

d u = u '   d x  and  v   =   ∫ d v

(d) For ∫ 3 x e 2 x we could choose u = 3 x and d v = e 2 x d x .

(a)

To determine

Whether the provided statement “In evaluating ∫udv parts, the parts u and dv are selected and the parts du and v are calculated”.

Explanation

Integration by parts is an integration technique that uses a formula that follows from the product rule of derivatives,

ddx(uv)=udvdx+vdudx

On integrating this formula by rearranging the differentials, the formula for integration by parts is obtained as,

∫udv=uv−∫vdu

Clearly, in the formula, the terms v and du are present, so yes, the parts u and dv are selected and the parts du and v are calculated.

For example, consider the integral,

∫1elnxdx

Now, split the integrand into two parts setting one part equal to u and another part equal to dv.

So, the values will be:

u=lnx

And,

dv=dx

Then,

du=1xdx

And,

v=

(b)

To determine

Whether the provided statement “In evaluating ∫udv by parts, the differential (often dx) is always chosen as a part of dv”.

(c)

To determine

Whether the provided statement “In evaluating ∫udv by parts, the parts du and v are found from u and dv as du=udx and v=∫dv.”

(d)

To determine

Whether the provided statement “For ∫3xe2xdx, the parts chosen can be u=3x and dv=e2xdx.”

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Chapter 13.5,
Problem 42E
Chapter 13.6,
Problem 2CP
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