Evaluating $int_0^l (lx-x^2)sinleft(fracnpi xlright),mathrmdx$ The Next CEO of Stack OverflowEvaluating the integral, $int_0^infty lnleft(1 - e^-xright) ,mathrm dx $Evaluating the definite integral $int_0^infty fracmathrme^xleft(mathrme^x-1right)^2,x^n ,mathrmdx$Evaluating $int_0^largefracpi4 logleft( cos xright) , mathrmdx $Can we simplify $int_0^pileft(fracsin nxsin xright)^mdx$?Assistance evaluating $int_0^2pifrac12left(2 sin theta + cos thetaright)dtheta$Evaluating $int_0^infty int_0^infty fracx^2 + y^21 + (x^2 - y^2)^2 e^-2xy :mathrmdx :mathrmdy$Closed form of $int_0^1int_0^1int_0^1fracleft(1-x^yright)left(1-x^zright)ln x(1-x)^3,mathrm dx;mathrm dy;mathrm dz$Evaluate :$int_0^1 frac1left(1+sqrtfrac1x-1right)(x^2-x-1)mathrm dx$Evaluating the integral: $intlimits_0^inftyleft(fracsin(ax)xright)^2 dx , a neq 0 $How to integrate $int_0^pi/2frac1sin^2(x)-sin(x)cos(x)+cos^2(x),mathrmdx$
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Evaluating $int_0^l (lx-x^2)sinleft(fracnpi xlright),mathrmdx$
The Next CEO of Stack OverflowEvaluating the integral, $int_0^infty lnleft(1 - e^-xright) ,mathrm dx $Evaluating the definite integral $int_0^infty fracmathrme^xleft(mathrme^x-1right)^2,x^n ,mathrmdx$Evaluating $int_0^largefracpi4 logleft( cos xright) , mathrmdx $Can we simplify $int_0^pileft(fracsin nxsin xright)^mdx$?Assistance evaluating $int_0^2pifrac12left(2 sin theta + cos thetaright)dtheta$Evaluating $int_0^infty int_0^infty fracx^2 + y^21 + (x^2 - y^2)^2 e^-2xy :mathrmdx :mathrmdy$Closed form of $int_0^1int_0^1int_0^1fracleft(1-x^yright)left(1-x^zright)ln x(1-x)^3,mathrm dx;mathrm dy;mathrm dz$Evaluate :$int_0^1 frac1left(1+sqrtfrac1x-1right)(x^2-x-1)mathrm dx$Evaluating the integral: $intlimits_0^inftyleft(fracsin(ax)xright)^2 dx , a neq 0 $How to integrate $int_0^pi/2frac1sin^2(x)-sin(x)cos(x)+cos^2(x),mathrmdx$
$begingroup$
I am stuck on evaluating the following definite integral:
$$int_0^l (lx-x^2)sinleft(fracnpi xlright) , mathrmdx$$
Aprreciate any help!
integration definite-integrals
edited Mar 18 at 13:31
StubbornAtom
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
$endgroup$
add a comment |
$begingroup$
I am stuck on evaluating the following definite integral:
$$int_0^l (lx-x^2)sinleft(fracnpi xlright) , mathrmdx$$
Aprreciate any help!
integration definite-integrals
edited Mar 18 at 13:31
StubbornAtom
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
$endgroup$
$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12
add a comment |
$begingroup$
I am stuck on evaluating the following definite integral:
$$int_0^l (lx-x^2)sinleft(fracnpi xlright) , mathrmdx$$
Aprreciate any help!
integration definite-integrals
edited Mar 18 at 13:31
StubbornAtom
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
$endgroup$
I am stuck on evaluating the following definite integral:
$$int_0^l (lx-x^2)sinleft(fracnpi xlright) , mathrmdx$$
Aprreciate any help!
integration definite-integrals
integration definite-integrals
edited Mar 18 at 13:31
StubbornAtom
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
edited Mar 18 at 13:31
StubbornAtom
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
edited Mar 18 at 13:31
StubbornAtom
6,30831440
edited Mar 18 at 13:31
StubbornAtom
6,30831440
edited Mar 18 at 13:31
StubbornAtom
6,30831440
6,30831440
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
asked Mar 18 at 13:10
mallorie000383mallorie000383
1
1
$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12
add a comment |
$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12
$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12
$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint:
$$int P(t)sin t,dt=-P(t)cos t+int P'(t)cos t,dt=-P(t)cos t+ P'(t)sin t,dt-int P''(t)cos t,dt.$$
Also notice that $P$ and the sine vanish at the bounds, so that only the last term remains.
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Hint:
$$int P(t)sin t,dt=-P(t)cos t+int P'(t)cos t,dt=-P(t)cos t+ P'(t)sin t,dt-int P''(t)cos t,dt.$$
Also notice that $P$ and the sine vanish at the bounds, so that only the last term remains.
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
Hint:
$$int P(t)sin t,dt=-P(t)cos t+int P'(t)cos t,dt=-P(t)cos t+ P'(t)sin t,dt-int P''(t)cos t,dt.$$
Also notice that $P$ and the sine vanish at the bounds, so that only the last term remains.
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
Hint:
$$int P(t)sin t,dt=-P(t)cos t+int P'(t)cos t,dt=-P(t)cos t+ P'(t)sin t,dt-int P''(t)cos t,dt.$$
Also notice that $P$ and the sine vanish at the bounds, so that only the last term remains.
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
$endgroup$
Hint:
$$int P(t)sin t,dt=-P(t)cos t+int P'(t)cos t,dt=-P(t)cos t+ P'(t)sin t,dt-int P''(t)cos t,dt.$$
Also notice that $P$ and the sine vanish at the bounds, so that only the last term remains.
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
answered Mar 18 at 13:30
Yves DaoustYves Daoust
131k676229
131k676229
add a comment |
add a comment |
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$begingroup$
Use Integration by parts en.wikipedia.org/wiki/Integration_by_parts
$endgroup$
– Mostafa Ayaz
Mar 18 at 13:12