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The figure composed of three line segments must be a triangle______ (judge right or wrong)
Because a closed figure composed of three line segments which are not on the same line are connected in sequence is called a triangle, the statement that the figure composed of three line segments must be a triangle is wrong
Let d be a plane area surrounded by the curve y = √ x, x + y = 2 and X axis, and find the volume V of the body of revolution formed by D rotating around the Y axis
The answer given by the teacher is 32 π / 15
First draw a graph and find the intersection point of the curve is (1,1). After the rotation, you can imagine doing many parallel planes perpendicular to the Y axis to intercept and rotate the body. The area of each plane obtained is solvable. In fact, it is to find the volume of the object whose parallel section is a known figure
If the parallel line of X axis y = Y0 intersects the original plane graph at two points, Y0 ∈ [0,1], then the length between the two points is 2-y0-y02, and the area after rotation is π (2-y0-y02) 2
So v = ∫ (0 to 1) π (2-y-y2) 2dy = π∫ (0 to 1) (4 + Y2 + y ^ 4-4y-4y2 + 2y3) dy = 17 π / 10
Can the area of the figure enclosed by Y & # 178; = 4x and the line y = 2X-4 be integrated on the x-axis? How to do it?
The integral problem is transformed into X & # 178; = 4Y and y = - # 189; X + 2
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