Reduction formule 1





A x b ( p x q ) n d x a x b p ( n 1 ) ( p x q ) n 1 a 2 p ( n 1 ) I n displaystyle int frac sqrt axb(pxq)n,textdx-frac sqrt axbp(n-1 pxq)n-1frac a2p(n-1)I_n!
And Jn : I n 1 sin a x ( n 2 ) x n 2 a n 2 J n 2 displaystyle I_n-1-frac sin ax(n-2)xn-2frac an-2J_n-2!
30 Start by setting: I n cos n x.I n f ( x, n ) d x, displaystyle I_nint f(x,n textdx, in terms of, i k f ( x, k ) d x, displaystyle I_kint f(x,k textdx, where.The Drag Reduction System allows drivers to open a gap in the rear wing at certain points during the race weekend, thereby removing much of the drag produced by the rear wing.I n e a x cos n 1 b x a 2 ( b n ) 2 ( a cos b x b n sin b x ) n ( n 1 ) b 2 a 2 ( b n ) 2 I.To supplement the example, the above can be used to evaluate the integral for (say) n 5; I 5 cos 5 x.Note that by the laws of indices : I n 1 2 I 2 n ( a x 2 b x c ) 2 n 1 2 d x 1 ( a x 2 b x c ) 2 n 1 d x displaystyle I_nfrac.An alternative way in which the derivation could be done starts by substituting e a x displaystyle eax.J n x n cos a x d x displaystyle J_nint xncos ax, textdx!In the race, a driver is also required to be within one second of the car in front at a detection point located prior to the DRS zone.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_n-frac x2a2(n-1 x2-a2)n-1-frac 2n-32a2(n-1)I_n-1!Applying this substitution we obtain: (2) beginalign int sin n x : dx - sinn-1 x cos x (n - 1)int (1 - sin 2 x) sin n-2 x : dx int sin n x : dx - sinn-1 x cos x (n - 1)int.I n x 2 a 2 ( n 1 ) ( a 2 x 2 ) n 1 2 n 3 2 a 2 ( n 1 ) I n 1 displaystyle I_nfrac x2a2(n-1 a2-x2)n-1frac 2n-32a2(n-1)I_n-1!
( p x q ) n a x b d x 2 ( p x q ) n 1 a x b p ( 2 n 3 ) b p a q p ( 2 n 3 ) I n displaystyle int (pxq)nsqrt axb, textdxfrac.
I zalando code promo 10 euros n, m d x x m ( a 2 x 2 ) n displaystyle I_n,mint frac textdxxm(a2-x2)n!




J n cos a x ( n 1 ) x n 1 a n 1 sin a x ( n 2 ) x n 2 a n 2 J n 2 displaystyle J_n-frac cos ax(n-1)xn-1-frac an-1left-frac sin ax(n-2)xn-2frac an-2J_n-2right!I n d x x n a x b displaystyle I_nint frac textdxxnsqrt axb!Integration by substitution: e a x d x d ( e a x ) a, displaystyle eax, textdxfrac textd(eax)a!Start by setting: I n x n e a x.Integral Reduction formula I n d x x n ( a x 2 b x c ) displaystyle I_nint frac textdxxn(ax2bxc!So the reduction formula is: x n e a x d x 1 a ( x n e a x n x n 1 e a x d x ).J n cos 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 sin n a x d x displaystyle I_nint sin nax, textdx!I n, m d x x m ( x 2 a 2 ) n displaystyle I_n,mint frac textdxxm(x2a2)n!In other words, the reduction formula expresses the integral.
Quadratic factors x 2 a 2 displaystyle x2-a2,!, for x a displaystyle x a!
N 1 displaystyle nneq 1!


[L_RANDNUM-10-999]
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