Обчислити площі фігур обмежені лініями: 1)у=√х,

Обчислити площі фігур обмежені лініями:
1)у=√х, х=4,у=0
2)у=2-х^3,у=1,×=-1×=1
3)у=×^2-4х+4,у=4-×^2
- Предмет:
  Алгебра
- Автор:
  jaidenrose
- 5 лет назад

Ответы 1

В 3 интеграле нужно найти точки пересечения двух функцийx^2-4x+4=4-x^22x^2-4x=02x(x-2)=0x=0 x=2 $1)\int\limits^4_0 { \sqrt{x}} \, dx =(2/3)x^{3/2} |(4;0)=(2/3)*4^{3/2}-((2/3)*0^{3/2})= \\ =(2/3)* \sqrt{32} = 8 \sqrt{2} /3 \\ 2)\int\limits^1_{-1} {(2-x^3)} \, dx-\int\limits^1_{-1} {(-1)} \, dx=2x-x^4/4|(1;-1)+x(1;-1)=\\=2-1/4-(-2-1/4)+1-(-1)=4+1+1=6\\ 3)\int\limits^2_0 {(4-x^2)} \, dx-\int\limits^2_0 {(x^2-4x+4)} \, dx=\int\limits^2_0 {(4-x^2-x^2+4x-4)} \, dx=\\=\int\limits^2_0 {(-2x^2+4x)} \, dx=(-(2/3)x^3+2x^2)|(2;0)=\\=-16/3+8-(-0+0)=(-16+24)/3=8/3$
- Автор:
  caitlinlawson
- 5 лет назад
- 0
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Обчислити площі фігур обмежені лініями: 1)у=√х, х=4,у=0 2)у=2-х^3,у=1,×=-1×=1 3)у=×^2-4х+4,у=4-×^2

Ответы 1

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Обчислити площі фігур обмежені лініями:
1)у=√х, х=4,у=0
2)у=2-х^3,у=1,×=-1×=1
3)у=×^2-4х+4,у=4-×^2