How to calculate the indefinite integral of $(x-1)^frac 12-(x-3)$?
Clash Royale CLAN TAG#URR8PPP
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
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 |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031674%2fhow-to-calculate-the-indefinite-integral-of-x-1-frac-12-x-3%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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 |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031674%2fhow-to-calculate-the-indefinite-integral-of-x-1-frac-12-x-3%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
