搜狗做题网英文微积分题目Let R be the smaller of the two regions enclosed by t
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英文微积分题目
Let R be the smaller of the two regions enclosed by the elipse 144x^2+16y^2=2304 and the line x=2^(3/2) . Find the area of the region R.
Let R be the smaller of the two regions enclosed by the elipse 144x^2+16y^2=2304 and the line x=2^(3/2) . Find the area of the region R.
这是一个在Y轴上的椭圆,要求的是与直线x=2^(3/2)围成的最小面积
把直线方程代入椭圆得y=±6√2
根据对称性,对x进行积分得
2∫[2^(3/2),4]√（144-9x^2)dx（直接用公式）
=2[1/3*3x/2*√（144-9x^2)+144/2arcsin(3x/12)][2^(3/2),4]
数值自己算吧
把直线方程代入椭圆得y=±6√2
根据对称性,对x进行积分得
2∫[2^(3/2),4]√（144-9x^2)dx（直接用公式）
=2[1/3*3x/2*√（144-9x^2)+144/2arcsin(3x/12)][2^(3/2),4]
数值自己算吧
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