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Calculus problem. Is my approach correct so far?

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Calculus problem. Is my approach correct so far? Empty Calculus problem. Is my approach correct so far?

Post by Rishi Fri May 10, 2013 6:55 pm

Someone posted this on the MIT open courseware website for the Calculus course

TenaciousT:
how do I deal with the square power in this problem:
Integrate: [ln(x))^2]
…


My approach

1. f(x) = [ln(x) ^ 2]

2. Let u = ln(x)

du/dx= 1/x

x*du = dx

[ln(x) ^ 2] = (u ^2) * (x * du)

Now x can be written as (e ^ ln(x))


∫[ln(x) ^ 2 dx] = ∫[(u ^ 2) * (e ^ u) du]





3. Then I can use the Integration by parts for solving ∫[(u ^ 2) * (e ^ u) du]





Rishi

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Calculus problem. Is my approach correct so far? Empty Re: Calculus problem. Is my approach correct so far?

Post by MaxEntropy_Man Fri May 10, 2013 7:12 pm

Rishi wrote:Someone posted this on the MIT open courseware website for the Calculus course

TenaciousT:
how do I deal with the square power in this problem:
Integrate: [ln(x))^2]
…


My approach

1. f(x) = [ln(x) ^ 2]

2. Let u = ln(x)

du/dx= 1/x

x*du = dx

[ln(x) ^ 2] = (u ^2) * (x * du)

Now x can be written as (e ^ ln(x))


∫[ln(x) ^ 2 dx] = ∫[(u ^ 2) * (e ^ u) du]





3. Then I can use the Integration by parts for solving ∫[(u ^ 2) * (e ^ u) du]





seems fine to me.
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