Question

= A circular region has a density of d(r) center of the circle. 1+p3 cm 2, where r is the distance from the If the radius of the entire circle is 20 centimeters, determine the mass of the shape. Show all work in evaluating your integral.

Answer 1

First we have to take small areal element of radius 'r' , then we have to write mass of small element.

Then integrate that mass with respect to 'r' and get whole mass of the shape.

DATE PAGE solution → Let a sto circle with density Se = e zoom x area Mass - density Mass (S(r)xdA 20, 0 20 Mass = 164/2.17 row) 44+3 + to get where dA = dlirdre small area have to integrate it whole XX wie Now, Let 3 idr 3 = راه = وام و 3 . Mass A 20 3 dx how of ser=0, x=0 A20 x = 8000

PAGE There fore, Mas = 8000 20 de 3 Lita 2 ln (1+x] = 21 (en (8001) - ln (1) 8000 3 21 X 8. 987 3 18.823 Mass = 18-823g