How to calculate the indefinite integral of $(x-1)^frac 12-(x-3)$?
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Why is the following integral wrong?
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12(x-3)^2+c $$
The answer given by my textbook is:
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12x^2+3x+c $$
I understand why the textbook's answer is right. But I don't understand what I did wrong in mine.
calculus integration indefinite-integrals
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
asked Dec 8 at 21:46
John Arg
266
add a comment |
up vote
3
down vote
favorite
Why is the following integral wrong?
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12(x-3)^2+c $$
The answer given by my textbook is:
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12x^2+3x+c $$
I understand why the textbook's answer is right. But I don't understand what I did wrong in mine.
calculus integration indefinite-integrals
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
asked Dec 8 at 21:46
John Arg
266
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Why is the following integral wrong?
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12(x-3)^2+c $$
The answer given by my textbook is:
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12x^2+3x+c $$
I understand why the textbook's answer is right. But I don't understand what I did wrong in mine.
calculus integration indefinite-integrals
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
asked Dec 8 at 21:46
John Arg
266
Why is the following integral wrong?
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12(x-3)^2+c $$
The answer given by my textbook is:
$$ int[(x-1)^frac 12-(x-3)]dx=frac 23 (x-1)^frac32-frac12x^2+3x+c $$
I understand why the textbook's answer is right. But I don't understand what I did wrong in mine.
calculus integration indefinite-integrals
calculus integration indefinite-integrals
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
asked Dec 8 at 21:46
John Arg
266
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
asked Dec 8 at 21:46
John Arg
266
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
edited Dec 9 at 1:53
AccidentalFourierTransform
1,427827
1,427827
asked Dec 8 at 21:46
John Arg
266
asked Dec 8 at 21:46
John Arg
266
asked Dec 8 at 21:46
John Arg
266
266
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
6
down vote
accepted
Note that
beginalign
frac23(x-1)^3/2-frac12(x-3)^2+c &= frac23(x-1)^3/2-frac12(x^2-6x+9)+c\ &= frac23(x-1)^3/2-frac12x^2+3xunderbrace-frac92+c_textconstant,
endalign
so both answers are valid.
answered Dec 8 at 21:48
MisterRiemann
5,7291624
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
accepted
Note that
beginalign
frac23(x-1)^3/2-frac12(x-3)^2+c &= frac23(x-1)^3/2-frac12(x^2-6x+9)+c\ &= frac23(x-1)^3/2-frac12x^2+3xunderbrace-frac92+c_textconstant,
endalign
so both answers are valid.
answered Dec 8 at 21:48
MisterRiemann
5,7291624
add a comment |
up vote
6
down vote
accepted
Note that
beginalign
frac23(x-1)^3/2-frac12(x-3)^2+c &= frac23(x-1)^3/2-frac12(x^2-6x+9)+c\ &= frac23(x-1)^3/2-frac12x^2+3xunderbrace-frac92+c_textconstant,
endalign
so both answers are valid.
answered Dec 8 at 21:48
MisterRiemann
5,7291624
add a comment |
up vote
6
down vote
accepted
up vote
6
down vote
accepted
Note that
beginalign
frac23(x-1)^3/2-frac12(x-3)^2+c &= frac23(x-1)^3/2-frac12(x^2-6x+9)+c\ &= frac23(x-1)^3/2-frac12x^2+3xunderbrace-frac92+c_textconstant,
endalign
so both answers are valid.
answered Dec 8 at 21:48
MisterRiemann
5,7291624
Note that
beginalign
frac23(x-1)^3/2-frac12(x-3)^2+c &= frac23(x-1)^3/2-frac12(x^2-6x+9)+c\ &= frac23(x-1)^3/2-frac12x^2+3xunderbrace-frac92+c_textconstant,
endalign
so both answers are valid.
answered Dec 8 at 21:48
MisterRiemann
5,7291624
edited Dec 8 at 21:54
answered Dec 8 at 21:48
MisterRiemann
5,7291624
answered Dec 8 at 21:48
MisterRiemann
5,7291624
answered Dec 8 at 21:48
MisterRiemann
5,7291624
5,7291624
add a comment |
add a comment |
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