J why boyther to define the Lebesgue do we integrad, wasn't the Riemann integrd good enough? Explain
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- Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.If C is the line segment that first connects point 2 to point i, and then the spring piece that connects point i to point -1 on the unit circle: Integral=?Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.
- Suppose the interval [2, 6] is partitioned into n = 4 subintervalswith grid points x0 = 2, x1 = 3, x2 = 4, x3 = 5, and x4 = 6.Write, but do not evaluate, the left, right, and midpoint Riemannsums for ƒ(x) = x2.Please show all work! https://www.geogebra.org/m/R4t3ZYrv#material/ZMb6uJ6KEvaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point (2,2) (see Figure 3).
- i want you to solve part C. remember from b, use the conclusion there, try to show as x in this open ball apporaching unit sphere, f should go to infinity. you prove that all boundary points goes to infinity.Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of radius r has volume equal to (4/3)(pi)(r^3).Determine whether each of the following statements is true or false, and explain why Simpson’s rule usually gives a better approximation than the trapezoidal rule.
- If UV bisects XY at point W, which statement must be true?Use the Intermediate Value Theorem to show that for all spheres with radii in the interval [5, 8], there is one with a volume of 1500 cubic centimeters.Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between the outward fluxesacross the two spheres?