Find the centroid of the region bounded by the given curves.

callaking2022-10-04 11:39:542条回答

Find the centroid of the region bounded by the given curves.
1.y=4x,x=7,x-axis
2.x+8y=8,y-axis,x-axis
3.y=7x,y=28,y-axis
4.y=x^2-16x,x-axis
5.16x-x^3,x-axis,第一象限
6.y=26x-x^2,y=x

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shuang3xia 共回答了14个问题 | 采纳率92.9%: 1.y=4x,x=7,x-axis
∫4xdx|[0,7]=2x^2|[0,7]=98
2、x+8y=8,y-axis,x-axis
y=1-x/8,0≤x≤8
∫（1-x/8）dx|[0,8]=x-1/16*x^2|[0,8]=4
3、 y=7x,y=28,y-axis
x=y/7
∫y/7dy|[0,28]=y^2/14|[0,28]=56
4、y=x^2-16x,x-axis
x^2-16x=0,x=0或16
∫（x^2-16x)dx|[16,0]=1/3*x^3-8x^2|[16,0]=2048/3
5、16x-x^3,x-axis,第一象限
16x-x^3＞0,x（x-4)(x+4)＜0
x＞0,所以积分范围为0＜x＜4
∫（16x-x^3）dx|[0,4]=8x^2-1/4*x^4|[0,4]=64
6、y=26x-x^2,y=x
代入得
x=26x-x^2,解得x1=25,x2=0,所以积分范围为[0,25]
∫(26x-x^2-x)dx|[0,25]=25/2*x^2-1/3x^3=15625/6; 1年前

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Find the centroid of the region bounded by the given curves.

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