Question

Convert the given integral to an equivalent integral in cylindrical coordinates and evaluate the result, 15 p/25-x² px² V x2 + y2 dz dy dx Jo

Answer 1

- Page 2 oft Solution → Page 1 of 4 Given integral 15,25-2, a pa Saty? dedyta we have to convert this integral into cylindrical coordinates we know cylindrical coordinates dady dz = 1Jl da dedz where - an,Y, 2) Jl. 91,9, 2) J = 122 22 22 h I lose assing are 2 = 360sa , y = 91 sine , ZEZ In cylindrical coordinates we see The region of integration is os 955, 038 371/2 and oczarcos expanding along Row -3 I = I lose tsine) = 1 (andydz = ndardedz On changing the given integral into cartesian coordinates substituting all these values in given integral

Page 3 of 4 " 1 Integral becomes Page 4 of 4 do dr is dasan? ("Watya dzdyda 910 90 90 -15 1/2 rocoso ਪਰ ਘਰ r=0 =0 2=0 x aida dodal pas endado del Bin T=0 = 15 l irose-o) do do = [(595_o = is the at cose doda 510 which is required answer