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4ymbarka
@4ymbarka
August 2022
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Обчісліть площу фігури,обмеженої лініями у=5-х2,у=х+3
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sangers1959
Verified answer
Y=5-x² y=x+3
5-x²=x+3
x²+x-2=0 D=9
x₁=-2 x₂=1
S=∫¹₋₂(5-x²-x-3)dx=∫¹₋₂(-x₂-x+2)dx=(-x³/3-x²/2+2x) |¹₋₂=-(x³/3+x²/2-2x) |¹₋₂=
=-(1³/3+1²/2-2*1-(-2)³/3-(-2)²/2+2*(-2))=-(1/3+1/2-2+2²/₃-2-4)=-(-4,5)=4,5.
Ответ: S=4,5 кв. ед.
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Answers & Comments
Verified answer
Y=5-x² y=x+35-x²=x+3
x²+x-2=0 D=9
x₁=-2 x₂=1
S=∫¹₋₂(5-x²-x-3)dx=∫¹₋₂(-x₂-x+2)dx=(-x³/3-x²/2+2x) |¹₋₂=-(x³/3+x²/2-2x) |¹₋₂=
=-(1³/3+1²/2-2*1-(-2)³/3-(-2)²/2+2*(-2))=-(1/3+1/2-2+2²/₃-2-4)=-(-4,5)=4,5.
Ответ: S=4,5 кв. ед.