Mixing
How can I calculate area enclosed by three curves in WolframAlpha?
0
$begingroup$
I'm trying to calculate the region enclosed by $y=frac{1}{x^2}$, $y=x$ and $y=4$ for $x in [frac{1}{2}, 4]$ How can I do this?
I know I can use definite integral for this task but I want a general formula that I can apply in WolframAlpha to check my calculations. Something like find area between y=1/x^2, y=x, y=4 from 1/2 to 4 but working. find area between y=1/x^2, y=x, y=4 works and returns (unbounded) as expected but I also need a way to specify interval.
wolfram-alpha
asked Jan 13 '18 at 16:18
MattMatt
17418
$endgroup$
add a comment |
0
$begingroup$
I'm trying to calculate the region enclosed by $y=frac{1}{x^2}$, $y=x$ and $y=4$ for $x in [frac{1}{2}, 4]$ How can I do this?
I know I can use definite integral for this task but I want a general formula that I can apply in WolframAlpha to check my calculations. Something like find area between y=1/x^2, y=x, y=4 from 1/2 to 4 but working. find area between y=1/x^2, y=x, y=4 works and returns (unbounded) as expected but I also need a way to specify interval.
wolfram-alpha
asked Jan 13 '18 at 16:18
MattMatt
17418
$endgroup$
$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43
add a comment |
0
0
0
$begingroup$
I'm trying to calculate the region enclosed by $y=frac{1}{x^2}$, $y=x$ and $y=4$ for $x in [frac{1}{2}, 4]$ How can I do this?
I know I can use definite integral for this task but I want a general formula that I can apply in WolframAlpha to check my calculations. Something like find area between y=1/x^2, y=x, y=4 from 1/2 to 4 but working. find area between y=1/x^2, y=x, y=4 works and returns (unbounded) as expected but I also need a way to specify interval.
wolfram-alpha
asked Jan 13 '18 at 16:18
MattMatt
17418
$endgroup$
I'm trying to calculate the region enclosed by $y=frac{1}{x^2}$, $y=x$ and $y=4$ for $x in [frac{1}{2}, 4]$ How can I do this?
I know I can use definite integral for this task but I want a general formula that I can apply in WolframAlpha to check my calculations. Something like find area between y=1/x^2, y=x, y=4 from 1/2 to 4 but working. find area between y=1/x^2, y=x, y=4 works and returns (unbounded) as expected but I also need a way to specify interval.
wolfram-alpha
wolfram-alpha
asked Jan 13 '18 at 16:18
MattMatt
17418
asked Jan 13 '18 at 16:18
MattMatt
17418
edited Jan 13 '18 at 16:31
Matt
asked Jan 13 '18 at 16:18
MattMatt
17418
asked Jan 13 '18 at 16:18
MattMatt
17418
asked Jan 13 '18 at 16:18
MattMatt
17418
17418
$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43
add a comment |
$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43
$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43
add a comment |
1 Answer
1
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oldest
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1
$begingroup$
The area is
$$int_{1/2}^1 left(4-frac{1}{x^2}right)dx+int_1^4(4-x),dx=frac{11}{2}.$$
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
$endgroup$
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something likefind area between y=1/x^2, y=x, y=4 from 0 to 4(this doesn't work though, just an example).
$endgroup$
– Matt
Jan 13 '18 at 16:33
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]
$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
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
1
$begingroup$
The area is
$$int_{1/2}^1 left(4-frac{1}{x^2}right)dx+int_1^4(4-x),dx=frac{11}{2}.$$
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
$endgroup$
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something likefind area between y=1/x^2, y=x, y=4 from 0 to 4(this doesn't work though, just an example).
$endgroup$
– Matt
Jan 13 '18 at 16:33
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]
$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
add a comment |
1
$begingroup$
The area is
$$int_{1/2}^1 left(4-frac{1}{x^2}right)dx+int_1^4(4-x),dx=frac{11}{2}.$$
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
$endgroup$
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something likefind area between y=1/x^2, y=x, y=4 from 0 to 4(this doesn't work though, just an example).
$endgroup$
– Matt
Jan 13 '18 at 16:33
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]
$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
add a comment |
1
1
1
$begingroup$
The area is
$$int_{1/2}^1 left(4-frac{1}{x^2}right)dx+int_1^4(4-x),dx=frac{11}{2}.$$
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
$endgroup$
The area is
$$int_{1/2}^1 left(4-frac{1}{x^2}right)dx+int_1^4(4-x),dx=frac{11}{2}.$$
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
answered Jan 13 '18 at 16:29
A. GoodierA. Goodier
3,60651427
3,60651427
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something likefind area between y=1/x^2, y=x, y=4 from 0 to 4(this doesn't work though, just an example).
$endgroup$
– Matt
Jan 13 '18 at 16:33
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]
$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
add a comment |
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something likefind area between y=1/x^2, y=x, y=4 from 0 to 4(this doesn't work though, just an example).
$endgroup$
– Matt
Jan 13 '18 at 16:33
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]
$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something like
find area between y=1/x^2, y=x, y=4 from 0 to 4 (this doesn't work though, just an example).$endgroup$
– Matt
Jan 13 '18 at 16:33
$begingroup$
Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something like
find area between y=1/x^2, y=x, y=4 from 0 to 4 (this doesn't work though, just an example).$endgroup$
– Matt
Jan 13 '18 at 16:33
1
1
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
$begingroup$
Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}]$endgroup$
– Awnon Bhowmik
Jan 13 '18 at 16:37
add a comment |
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$begingroup$
Maybe because area is unbounded. See the plot: wolframalpha.com/input/?i=y%3Dx,+y%3D1%2Fx%5E2,+y%3D4 I cannot identify a bounded area.
$endgroup$
– callculus
Jan 13 '18 at 16:25
$begingroup$
Wolfram products have serious issues that they have little interest in fixing.
$endgroup$
– Cameron Williams
Jan 13 '18 at 16:25
$begingroup$
@callculus - You're right, I edited the question.
$endgroup$
– Matt
Jan 13 '18 at 16:28
$begingroup$
@user509051 There is no other choice than calculate them seperately: First area and Second area Then add the values.
$endgroup$
– callculus
Jan 13 '18 at 17:43