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Calculus
- Setup, but don't evaluate, the integrals which give the volume of the solid formed by revolving the region bounded by y = x2+1, y = x, x = 1, x = 2 about these lines: a) x = -3 b) x = 4 c) x = 1arrow_forwardSet-up the iterated double integral in rectangular coordinates equalto the volume of the solid in the first octant bounded above by the paraboloid z = 1−x2-y2, below by the plane z =3/4, and on the sides by the planes y = x and y = 0.arrow_forwardRefer to the iterated triple integral below. a. Setup the equivalent iterated integral in cylindrical coordinates b. Sketch the solid of integration for the given iterated integral.arrow_forward
- Using the solid region description, give the integral for a) the mass, b) the center of mass, and c) the moment of inertia about the z axis The solid in the first octant bounded by the coordinate planes and x2 + y2 + z2 = 25 with density function p=kxyarrow_forwardConverting to a polar integral Integrate ƒ(x, y) = [ln (x2 + y2 ) ]/sqrt(x2 + y2) over the region 1<= x2 + y2<= e.arrow_forwarduse a CAS integration utility to evaluate the triple integral of the given function over the specified solid region. F(x, y, z) = z/(x2 + y2 + z2)^3/2 over the solid bounded below by z the cone z = sqrt(x2 + y2) and above by the plane z = 1arrow_forward
- IntegrationDetermine the volume of the solid below the paraboloid z=x²+3y² and above the region bounded by the planes x=0 ,y=1,y=x and z=0arrow_forwardUsing geometry, calculate the volume of the solid under z=√49−x2 −y2 and over the circular disk x2 +y2 ≤49.arrow_forwardSketch and shade the region enclosed between y=(1/2)x^2 and y=xsqrt(x). a. Rotate the region about x axis and setup an integral that gives the volume of the solid of revolution. b. Rotate the region about y axis and setup an integral that gives the volume of the solid of revolution. c. Rotate the region about y= -1 and setup an integral that gives the volume of the solid of revolution.arrow_forward
- using double integration, find the area A(F) of the region F={(x,y): y2≤ x≤ 4, 0≤ y≤ 2}arrow_forwarduse a CAS integration utility to evaluate the triple integral of the given function over the specified solid region. F(x, y, z) = x4 + y2 + z2 over the solid sphere x2 + y2+z2 <= 1arrow_forwardSetup an integral for volume bounded by z = -1, y = x3, y = 4x, and z = 10 + x2 + y2arrow_forward
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