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Use fundamental theorem of calculus to compute definite integral

  • Thread starter s3a
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  • #1
s3a
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Homework Statement


The problem and my (incorrect) work are typed and attached as TheProblemAndMyWorkTypedUp.jpg.

Homework Equations


Integral from a to b of f(t) = F(b) – F(a)

The Attempt at a Solution


As mentioned above, my work is attached as TheProblemAndMyWorkTypedUp.jpg. (The (2 – 1)^12 part “dissappeared” because d/dx (constant) = 0.)

Could someone please help me figure out why what I did is wrong?
 

Attachments

Answers and Replies

  • #2
UltrafastPED
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Replace t with x^2; then t^2 = x^4.
 
  • #3
verty
Homework Helper
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I think you need to change t so that your upper limit is x. Then I think your argument will go through.
 
  • #4
s3a
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Oh, yes, I jumped the gun with assuming it was just x on the upper limit of the integral!

So, this (=the attachment of this reply) is how I do it, right?
 

Attachments

  • #5
CAF123
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Oh, yes, I jumped the gun with assuming it was just x on the upper limit of the integral!

So, this (=the attachment of this reply) is how I do it, right?
Since the upper limit is a function of x, you have to apply chain rule. Straightforward application of FTOC can only be applied when the upper limit is just x and the lower limit a constant.
 
  • #6
s3a
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So, is this (=the attachment of this reply) how it's done?
 

Attachments

  • #7
CAF123
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So, is this (=the attachment of this reply) how it's done?
Correct :smile:
 
  • #8
s3a
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Yay! Thank you! :)
 

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