Math Is Fun Forum

Q1 - Evaluate the iterated integral by converting to polar coordinates

∫0 to 2 ∫-Sqrt 4-x^2 to Sqrt 4-x^2 e^(-x^2-y^2) dy dx

The region of integration is bounded by
-Sqrt 4-x^2 ≤ y ≤ Sqrt 4-x^2 and 0 ≤ x ≤ 2

Q2 - Evaluate the triple integral ∫∫R∫ OR ∫∫∫R f(x,y,z)dV

With f(x,y,z)=Sqrt y -3z^2

Q = {(x,y,z)/2 ≤ x ≤ 3, 0≤ y ≤1, -1≤ z ≤1 }

Q1 - Use chain rule to find df/dx , df/dy

For f(r,s,v) = r^3 + s + v^2  ,  where r = xe^y  , s = ye^x and v = x^2 y

Q2 - Spherical coordinates of a point are (4 , π/6 , π/2)

a - Convert spherical coordinates to rectangular coordinates

b - Convert spherical coordinates to cylinderical coordinates

c - Verify your answer by converting back spherical coordinates from anyone of these, that is , either from rectangular or cylinderical coordinates.

I need detailed answer for Question no. 1 coz i dont know how to start it.. and for Question 2 just hints for that .. Thanks in advance

Determine whether the series:

Can I have some hints in solving this question..:/

Q1 - Find the volume of the solids generated by revolving the regions bounded by the lines and curves about x-axis

y=√cosx where 0 ≤ x ≤ π/2 and y=0 , x=0

Q2 - Evaluate the integral

Thanx in adavnce...

Q1- The distance traveled by an object at time t ≥ 0 is s = f(t) = t^2 where s is in meter (m) and t in seconds (sec). Find the instantaneous velocity of the object at t = 2sec

Q2- Find the natural domain of the given function

h(x) = 1/1-sinx

Q3- What are the points of discontinuity for the function f(x)=x+5/x^2-1 ?