Calc 3, Chapter 15 Combine the sum of two double integrals xydydx+xy dydx into a

Question

Calc 3,

Chapter 15

Combine the sum of two double integrals xydydx+xy dydx into a single double integral by converting to polar coordinates. Evaluate the resulting double integral First precisely graph the region of integration. Find the volume of the solid in the first octant bounded above by the cone z = below by Z = 0. and laterally by the cylinder X2 + y2 =2y. Use polar coordinates. First precisely graph the region of integration. Evaluate the iterated integral dxdy by first reversing the order of integration Find the centroid (center of mass) of the region that is enclosed between y =[x] and y=4 First, precisely graph the region of integration. Given the triple integral f(x,y,z)dzdydx rewrite the integral in five remaining orders of integration. First, sketch the solid as precisely as possible and then graph three projections to the coordinate planes.. .) The solid enclosed by the surface Z = 1 - y2 (assume y > 0) and the planes z = 0,.x = -1, x = 1 has density Delta (x,y,z) = yz. Find the center of mass of the solid

Explanation / Answer

when we reverse the order of integration now X varies from 0 to 2 and Y varies from 0 to x^2 now the integral changes from int (0 to 2)inte (0 to X^2)[(exp^x^3)dy dx]...we can now separate the variables easily ....by evaluating dy first we get ,,,,,,int (0 to 2) [X^2)(exp^x^3)]dx....now putting x^3 is in exp and we have its derivative so ,,,,,,,we can easily evaluate the integral as shown ......Putting x^3 as a variable t ,,,,,,,we get the integral as...,int (0 to 8) [exp^t)/3]dx...we get (exp ^8-1)/3

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---