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Mathematical Applications for the ...

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

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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=uvvdu

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 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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