aniq integralning geometriyaga tatbiqlari

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1576220695.doc ò - = b a dx x f s ) ( ò = b a dx x f s | ) ( | dx x x f s b a ò - = )] ( ) ( [ j ò - = b a dx x x f s | ) ( ) ( | j ò - = c a dx x x f s )] ( ) ( [ 1 j ò - = b c ii dx x x s )] ( ) ( [ j y ò - = d c iii dx x x f s )] ( ) ( [ a 3 32 0 4 ] 3 3 2 [ ] 4 [ )] ( 3 [ 2 4 0 2 4 0 2 = - = - = - - - = ò ò x x dx x x dx x x …
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:= interface_plot ( ... ) s2 := interface_plot ( ... ) s1 := 3 2 p s2 := 9 4 p s := 3 4 p 3 / 2 3 / 2 3 / 2 a y x = + p p p p 2 2 / 0 2 2 2 / 0 2 2 2 2 / 0 8 3 2 sin 2 3 sin cos 3 2 ) ( 2 1 * 4 1 a dt t a dt t t a dt x y y x s = = = ¢ - ¢ = ò ò ò x := t / a cos ( t ) 3 y := t / a sin ( t ) 3 s := 3 8 a 2 p å = d » n i i i x s v 1 ) ( x 0 max ® d = i i x …
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05 32 ) 9 1 7 3 5 3 3 1 ( 6 0 2 / ) sin 9 1 sin 7 3 sin 5 3 sin 3 1 ( 6 2 2 9 7 5 3 2 a a t t t t a p p p p = - + - = - + - 32 105 p x := t / a cos ( t ) 3 y := t / a sin ( t ) 3 vy := 32 105 p a 3 32 105 p dt t t l b a t t ò + = 2 2 )) ( ' ( )) ( ' ( y j ò + = b a dx x f l 2 )) ( ' ( 1 î í ì = = j r j r sin , cos y x ò + = b a j r r …
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p p = ÷ ÷ ø ö ç ç è æ ÷ ÷ ø ö ç ç è æ + - ÷ ÷ ø ö ç ç è æ + × = ÷ ÷ ø ö ç ç è æ + × = 3 3 2 1 3 4 1 1 4 1 2 3 4 4 1 3 2 2 p p x . 283 , 8 6 5 5 27 8 5 5 8 27 3 4 » - = ÷ ÷ ø ö ç ç è æ - = p p k 5 6 5 p c 9 2 p 2 x y = k 5 6 5 p c 17 6 17 p 2 3 2 , 2 x y x y = - = 1 6 p ( 5 5 k 1 ) c 28 81 p 13 k 8 243 p ln ( 2 …
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mda oa va ob lar) bilan chegaralangan shakl egri chiziqli sektor deb ataladi. xususiy holda (=f(() grafigi aylana yoyidan (ya’ni (=r- o‘zgarmas) iborat bo‘lsa,u doiraviy sektor bo‘ladi. bunday egri chiziqli sektor yuzini hisoblash masalasini qo‘yib, [(;(] kesmani ixtiyoriycha qilib, n ta bo‘laklarga (=(0 with(plots): > implicitplot(r=abs(cos(phi)), r=-1..1, phi =0..2*pi, coords=polar,thickness=2,title=`bernuli lyumniskatasi`); 12.8 –rasm. > restart; > with(integrationtools): s := int((cos(phi)^2)/2, phi=0..2*pi); > value(%); > evalf(s,5); 1.5708 15-misol. qutb koordinatalari sistemasida (=a aylana va (=2acos3( uch yaproq chiziqlari bilan chegaralangan aylana tashqarisida hosi bo’lgan yuzalarni hisoblang. yechish. (=2acos3( chiziq t=2π/3 davr bilan [-π, π] da chiziq quriladi. unda cos3(≥0 ekanidan birinch bo’lagi [-π/6, π/6] oraloqda joylashgan. bu bo’lakning aylana bilan kesishish niqtalari 2acos3( =a tenglamadan (1=-π/9, (2=π/9 bo’lasi. > restart; > with(plots): polarplot([1,2*cos(3*t)],t=0..2*pi,color= [blue,red], thickness=2); > p1:=phi->a; p2:=phi->2*a*cos(3*phi); > s3:=(1/2)*int(p2(phi)^2-p1(phi)^2, phi=-pi/.pi/9); > a:=1:s3:value(%); > evalf(%); 0.6377409851 tekisligida parametrik tenglamalar bilan berilgan chiziq bilan chegaralgan tekis shakl yuzini hisoblash. aytaylik, dekart koordinatalar …

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1576220695.doc ò - = b a dx x f s ) ( ò = b a dx x f s | ) ( | dx x x f s b a ò - = )] ( ) ( [ j ò - = b a dx x x f s | ) ( ) ( | j ò - = c a dx x x f s )] ( ) ( [ 1 j ò - = b c ii dx x x s )] ( ) ( [ j y ò - = d c iii dx x x f s )] ( ) ( [ a 3 32 0 4 ] 3 3 2 [ ] 4 [ …

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