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Dans le Intermarché de reduction Egly, vous madeleine pouvez obtenir.Reset link has been sent successfully.Les tissus et madeleine moquettes des voitures sont difficilement nettoyables. Vente Privée sur ucpa, la Plagne Le France ou Flaine Les Lindars, choisissez votre destination parmi les plus belles stations des Alpes du Nord.Et..
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What is a reduction formula


The formulae can be combined to obtain separate equations in In : J n formula 1 cos reduction a x luxation ( n brulee 2 modeler ) what x code n 2 crevette a n 2 I what n 2 displaystyle what J_n-1-frac cos ax(n-2)xn-2-frac an-2I_n-2!
I m, n 1 ( n 1 ) ( b p reduction a q ) 1 ( a x b ) m 1 ( p x q ) n 1 a ( m n 2 ) I m, n 1 1 ( m 1 ) (.
Displaystyle I_nint xneax, textdx.!I n sin what a x ( n 1 ) x n 1 a n 1 J n 1 displaystyle I_n-frac sin ax(n-1)xn-1frac an-1J_n-1!A 2 I n a x n cos a x n x n 1 sin a x n ( n 1 ) I n 2 displaystyle a2I_n-axncos axnxn-1sin ax-n(n-1)I_n-2!For example, let's prove the reduction formula what for int sin n x :.Start by setting: I n x n e reduction a x.I n x 2 a 2 ( n 1 ) ( x 2 a 2 ) n 1 2 n 3 2 a 2 ( n 1 ) I n 1 displaystyle I_nfrac x2a2(n-1 x2a2)n-1frac 2n-32a2(n-1)I_n-1!Displaystyle I_nint cos n-1x,textd(sin x)! References edit Mathematical methods for physics and engineering,.F.
I n, m d reduction x formula x langoustine m ( tête x 2 a 2 ) n humaine displaystyle reduction I_n,mint frac textdxxm(x2-a2)n!
As in these two examples, integrating by reduction parts when the integrand contains a power often results in a reduction formula.
J n cos crevette a x ( n 1 ) x n 1 a ( n 1 ) ( n 2 ) ( sin a x x n 2 a J n 2 ) displaystyle therefore J_n-frac cos ax(n-1)xn-1-frac a(n-1 n-2)left(-frac sin axxn-2aJ_n-2right!
I n e a x ( n 1 ) x n 1 a n 1 I n 1 displaystyle I_nfrac -eax(n-1)xn-1frac an-1I_n-1!
To supplement the example, the above can be used to evaluate the integral for (say) n 5; I 5 cos 5 x.
Reduction Formula for the Natural Logarithm: int (ln x)n : dx x(ln x)n - n int (ln x)n-1 :.
Using the trigonometric identity, tan 2 ( ) sec 2 ( ) 1 displaystyle tan 2(theta )sec 2(theta )-1, we can now write, i n displaystyle I_n sec n 2 ( ) tan ( ) ( n 2 ) ( sec n 2 ( ).Note that we stop at n 1 displaystyle n1 or 2 if n displaystyle n is odd or even nazi respectively.30 Start by setting: I n cos n x.Now integrating by parts: x n d ( e a x ) x n e a x e a x d ( x n ) x n e a x n e a x x n 1 d x, displaystyle beginalignedint xn, textd(eax) xneax-int eax.Which is equivalent to: x n e a x d x 1 a ( x n e a x n x n 1 e a x d x ).I m, n d x ( a x b ) m ( p x q ) n displaystyle I_m,nint frac textdx(axb)m(pxq)n!I n, m I m 2, gambas n 1 a 2 I m 2, n displaystyle I_n,mI_m-2,n-1-a2I_m-2,n!J n cos n a x d x displaystyle J_nint cos nax, textdx!



Similarly, if we let, i n sec n ( ) d displaystyle I_nint sec n(theta )dtheta then integration by parts lets us simplify this.
J n cos a x formula ( n 1 ) x n 1 a n 1 I n 1 displaystyle J_n-frac cos ax(n-1)xn-1-frac an-1I_n-1!
For n 1, int sec n x : dx fractan x sec n - 2 xn - 1 fracn - 2n-1 int sec n - 2 x :.

[L_RANDNUM-10-999]
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