Calculate the following integral: $int_0^2pi sqrtcos^2t + 9sin^2t, dt$ Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Compute $int_0^fracpi2fracsin^2xcos xsin x+cos xdx$Calculating the following integral using complex analysis: $int_0^pie^acos(theta)cos(asin(theta)), dtheta$How to calculate $int_0^2pi sin(x)(cos x+sqrt2-cos(x));mathrm dx$ with substitution?Definite Integral $int_-pi^pifrace^sin(x)+cos(x)cos(sin(x))e^sin(x)+e^xdx$How find this integral $intfracsinxsqrt2+sinx+cosxdx$Calculus Question: Improper integral $int_0^inftyfraccos(2x+1)sqrt[3]xdx$Integral with simple fractions: $int_ fraccos x sin x sqrt1+cos^2x , dx$How to evaluate $int_0^2pidx!int_0^pisin ye^sin y(cos x-sin x)dy=sqrt2big(e^sqrt2-e^-sqrt2big)pi $Find $ int cos(x) sqrt1+sin^2(x) dx$$int_pi/6^pi/3 (sin x + cos x) / sqrtsin(2x), dx$
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Calculate the following integral: $int_0^2pi sqrtcos^2t + 9sin^2t, dt$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Compute $int_0^fracpi2fracsin^2xcos xsin x+cos xdx$Calculating the following integral using complex analysis: $int_0^pie^acos(theta)cos(asin(theta)), dtheta$How to calculate $int_0^2pi sin(x)(cos x+sqrt2-cos(x));mathrm dx$ with substitution?Definite Integral $int_-pi^pifrace^sin(x)+cos(x)cos(sin(x))e^sin(x)+e^xdx$How find this integral $intfracsinxsqrt2+sinx+cosxdx$Calculus Question: Improper integral $int_0^inftyfraccos(2x+1)sqrt[3]xdx$Integral with simple fractions: $int_ fraccos x sin x sqrt1+cos^2x , dx$How to evaluate $int_0^2pidx!int_0^pisin ye^sin y(cos x-sin x)dy=sqrt2big(e^sqrt2-e^-sqrt2big)pi $Find $ int cos(x) sqrt1+sin^2(x) dx$$int_pi/6^pi/3 (sin x + cos x) / sqrtsin(2x), dx$
$begingroup$
I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$
I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$
but now I don't know how to continue with the solution.
calculus integration
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
$endgroup$
|
show 1 more comment
$begingroup$
I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$
I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$
but now I don't know how to continue with the solution.
calculus integration
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
$endgroup$
$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05
|
show 1 more comment
$begingroup$
I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$
I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$
but now I don't know how to continue with the solution.
calculus integration
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
$endgroup$
I have the following integral:
$$int_0^2pi sqrtcos^2t + 9sin^2t, dt$$
I used $cos^2t + sin^2t=1$ and $2sin^2t=1-cos2t$ so I got:
$$int_0^2pi sqrt5-4cos2t , dt$$
but now I don't know how to continue with the solution.
calculus integration
calculus integration
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
edited Mar 26 at 18:15
Thomas Shelby
4,7832727
4,7832727
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
asked Mar 26 at 18:13
Dr.MathematicsDr.Mathematics
516
516
$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05
|
show 1 more comment
$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05
$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05
|
show 1 more comment
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$begingroup$
This looks like the perimeter of an ellipse which usually cannot be determined exactly.
$endgroup$
– Peter Foreman
Mar 26 at 18:15
$begingroup$
see complete elliptic integral of 2nd kind
$endgroup$
– achille hui
Mar 26 at 18:18
$begingroup$
Wikipedia also explains how one might compute the circumference of an ellipse on this page
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
According to the google plugin, the answer is about $13.36$.
$endgroup$
– Omnomnomnom
Mar 26 at 18:19
$begingroup$
I had to calculate the length of the curve $(sint, 3cost)$ for these $t$, that's why I got the integral. I don't know why our teacher give us this exercise since I am on my second semester at university and I don't really know what "elliptic integral of 2nd kind" is.
$endgroup$
– Dr.Mathematics
Mar 26 at 19:05