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Evaluating $int_0^l (lx-x^2)sinleft(frac{npi x}{l}right),mathrm{d}x$

Evaluating the integral, $int_{0}^{infty} lnleft(1 - e^{-x}right) ,mathrm dx $Evaluating the definite integral $int_0^infty frac{mathrm{e}^x}{left(mathrm{e}^x-1right)^2},x^n ,mathrm{d}x$Evaluating $int_0^{largefrac{pi}{4}} logleft( cos xright) , mathrm{d}x $Can we simplify $int_0^{pi}left(frac{sin nx}{sin x}right)^mdx$?Assistance evaluating $int_0^{2pi}frac{1}{2}left(2 sin theta + cos thetaright)dtheta$Evaluating $int_0^infty int_0^infty frac{x^2 + y^2}{1 + (x^2 - y^2)^2} e^{-2xy} :mathrm{d}x :mathrm{d}y$Closed form of $int_0^1int_0^1int_0^1frac{left(1-x^yright)left(1-x^zright)ln x}{(1-x)^3},mathrm dx;mathrm dy;mathrm dz$Evaluate :$int_0^1 frac{1}{left(1+sqrt{frac{1}{x}-1}right)(x^2-x-1)}mathrm dx$Evaluating the integral: $intlimits_{0}^{infty}left(frac{sin(ax)}{x}right)^2 dx , a neq 0 $How to integrate $int_0^{pi/2}frac{1}{sin^2(x)-sin(x)cos(x)+cos^2(x)},mathrm{d}x$

-2

$begingroup$

I am stuck on evaluating the following definite integral:

$$int_0^l (lx-x^2)sinleft(frac{npi x}{l}right) , mathrm{d}x$$

Aprreciate any help!

integration definite-integrals

share|cite|improve this question

edited Mar 18 at 13:31

StubbornAtom

6,29831440

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 | 

-2

$begingroup$

I am stuck on evaluating the following definite integral:

$$int_0^l (lx-x^2)sinleft(frac{npi x}{l}right) , mathrm{d}x$$

Aprreciate any help!

integration definite-integrals

share|cite|improve this question

edited Mar 18 at 13:31

StubbornAtom

6,29831440

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:

$$int_0^l (lx-x^2)sinleft(frac{npi x}{l}right) , mathrm{d}x$$

Aprreciate any help!

integration definite-integrals

share|cite|improve this question

edited Mar 18 at 13:31

StubbornAtom

6,29831440

asked Mar 18 at 13:10

mallorie000383mallorie000383

1

$endgroup$

share|cite|improve this question

edited Mar 18 at 13:31

StubbornAtom

6,29831440

asked Mar 18 at 13:10

mallorie000383mallorie000383

1

share|cite|improve this question

edited Mar 18 at 13:31

StubbornAtom

6,29831440

asked Mar 18 at 13:10

mallorie000383mallorie000383

1

edited Mar 18 at 13:31

StubbornAtom

6,29831440

edited Mar 18 at 13:31

StubbornAtom

6,29831440

asked Mar 18 at 13:10

mallorie000383mallorie000383

1

asked Mar 18 at 13:10

mallorie000383mallorie000383

1

1 Answer
1

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oldest

votes

0

$begingroup$

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.

share|cite|improve this answer

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

$endgroup$

add a comment | 

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0

$begingroup$

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.

share|cite|improve this answer

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

$endgroup$

add a comment | 

0

$begingroup$

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.

share|cite|improve this answer

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

$endgroup$

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.

share|cite|improve this answer

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

$endgroup$

share|cite|improve this answer

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229

answered Mar 18 at 13:30

Yves DaoustYves Daoust

132k676229