Evaluate $int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$ [duplicate]
This question already has an answer here:
Integrating $ int_2^4 frac{ sqrt{ln(9-x)} }{ sqrt{ln(9-x)}+sqrt{ln(x+3)} } dx. $
2 answers
Help with the evaluation of this definite integral. I don't know where to start.
So we have :$frac{sqrt{ln(9-x)}}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=frac{ln(9-x)-sqrt{ln(9-x)}sqrt{ln(x+3)} }{ln(9-x)-ln(x+3)}$ What's now?
calculus
edited Nov 23 at 14:30
user376343
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
marked as duplicate by Nosrati, Saad, lab bhattacharjee calculus
Users with the calculus badge can single-handedly close calculus questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Nov 23 at 18:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
This question already has an answer here:
Integrating $ int_2^4 frac{ sqrt{ln(9-x)} }{ sqrt{ln(9-x)}+sqrt{ln(x+3)} } dx. $
2 answers
Help with the evaluation of this definite integral. I don't know where to start.
So we have :$frac{sqrt{ln(9-x)}}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=frac{ln(9-x)-sqrt{ln(9-x)}sqrt{ln(x+3)} }{ln(9-x)-ln(x+3)}$ What's now?
calculus
edited Nov 23 at 14:30
user376343
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
marked as duplicate by Nosrati, Saad, lab bhattacharjee calculus
Users with the calculus badge can single-handedly close calculus questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Nov 23 at 18:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
1
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
1
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
1
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36
add a comment |
This question already has an answer here:
Integrating $ int_2^4 frac{ sqrt{ln(9-x)} }{ sqrt{ln(9-x)}+sqrt{ln(x+3)} } dx. $
2 answers
Help with the evaluation of this definite integral. I don't know where to start.
So we have :$frac{sqrt{ln(9-x)}}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=frac{ln(9-x)-sqrt{ln(9-x)}sqrt{ln(x+3)} }{ln(9-x)-ln(x+3)}$ What's now?
calculus
edited Nov 23 at 14:30
user376343
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
This question already has an answer here:
Integrating $ int_2^4 frac{ sqrt{ln(9-x)} }{ sqrt{ln(9-x)}+sqrt{ln(x+3)} } dx. $
2 answers
Help with the evaluation of this definite integral. I don't know where to start.
So we have :$frac{sqrt{ln(9-x)}}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=frac{ln(9-x)-sqrt{ln(9-x)}sqrt{ln(x+3)} }{ln(9-x)-ln(x+3)}$ What's now?
This question already has an answer here:
Integrating $ int_2^4 frac{ sqrt{ln(9-x)} }{ sqrt{ln(9-x)}+sqrt{ln(x+3)} } dx. $
2 answers
calculus
calculus
edited Nov 23 at 14:30
user376343
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
edited Nov 23 at 14:30
user376343
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
edited Nov 23 at 14:30
user376343
2,7782822
edited Nov 23 at 14:30
user376343
2,7782822
edited Nov 23 at 14:30
user376343
2,7782822
2,7782822
asked Nov 23 at 14:28
mathnoob
1,759422
asked Nov 23 at 14:28
mathnoob
1,759422
asked Nov 23 at 14:28
mathnoob
1,759422
1,759422
marked as duplicate by Nosrati, Saad, lab bhattacharjee calculus
Users with the calculus badge can single-handedly close calculus questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Nov 23 at 18:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Nosrati, Saad, lab bhattacharjee calculus
Users with the calculus badge can single-handedly close calculus questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Nov 23 at 18:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
1
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
1
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
1
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36
add a comment |
1
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
1
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
1
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
1
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36
1
1
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
1
1
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
1
1
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
1
1
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36
add a comment |
1 Answer
1
active
oldest
votes
$displaystyle int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=I=int_{2}^{4}frac{sqrt{ln(x+3)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$
$displaystyleimplies 2I=int_{2}^{4}frac{sqrt{ln(9-x)}+sqrt{ln(x+3)} :dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=int_{2}^{4} dx=2implies I=1.$
$left(text{Using }:displaystyleint_a^bf(x)dx=int_a^bf(a+b-x)dxright)$.
answered Nov 23 at 15:34
Yadati Kiran
1,694519
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$displaystyle int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=I=int_{2}^{4}frac{sqrt{ln(x+3)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$
$displaystyleimplies 2I=int_{2}^{4}frac{sqrt{ln(9-x)}+sqrt{ln(x+3)} :dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=int_{2}^{4} dx=2implies I=1.$
$left(text{Using }:displaystyleint_a^bf(x)dx=int_a^bf(a+b-x)dxright)$.
answered Nov 23 at 15:34
Yadati Kiran
1,694519
add a comment |
$displaystyle int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=I=int_{2}^{4}frac{sqrt{ln(x+3)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$
$displaystyleimplies 2I=int_{2}^{4}frac{sqrt{ln(9-x)}+sqrt{ln(x+3)} :dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=int_{2}^{4} dx=2implies I=1.$
$left(text{Using }:displaystyleint_a^bf(x)dx=int_a^bf(a+b-x)dxright)$.
answered Nov 23 at 15:34
Yadati Kiran
1,694519
add a comment |
$displaystyle int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=I=int_{2}^{4}frac{sqrt{ln(x+3)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$
$displaystyleimplies 2I=int_{2}^{4}frac{sqrt{ln(9-x)}+sqrt{ln(x+3)} :dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=int_{2}^{4} dx=2implies I=1.$
$left(text{Using }:displaystyleint_a^bf(x)dx=int_a^bf(a+b-x)dxright)$.
answered Nov 23 at 15:34
Yadati Kiran
1,694519
$displaystyle int_{2}^{4}frac{sqrt{ln(9-x)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=I=int_{2}^{4}frac{sqrt{ln(x+3)} dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}$
$displaystyleimplies 2I=int_{2}^{4}frac{sqrt{ln(9-x)}+sqrt{ln(x+3)} :dx}{sqrt{ln(9-x)}+sqrt{ln(x+3)}}=int_{2}^{4} dx=2implies I=1.$
$left(text{Using }:displaystyleint_a^bf(x)dx=int_a^bf(a+b-x)dxright)$.
answered Nov 23 at 15:34
Yadati Kiran
1,694519
answered Nov 23 at 15:34
Yadati Kiran
1,694519
answered Nov 23 at 15:34
Yadati Kiran
1,694519
answered Nov 23 at 15:34
Yadati Kiran
1,694519
1,694519
add a comment |
add a comment |
1
Use math.stackexchange.com/questions/439851/…
– lab bhattacharjee
Nov 23 at 14:30
1
math.stackexchange.com/questions/578957/…
– lab bhattacharjee
Nov 23 at 14:33
1
Also math.stackexchange.com/questions/957510
– Nosrati
Nov 23 at 14:36
1
math.stackexchange.com/questions/1073120/…
– lab bhattacharjee
Nov 23 at 14:36