SKEDSOFT

Maths For Engineers - 1

Problems on Integrals-1:

7. Find the area of the circle x2 y2 = a2. by using the double integrals.

Solution: Since the circle is symmetric about the coordinates axes, area of circle is 4 times the area OAB as shown in the figure. For the region OAB, y varies from 0 to and x varies from 0 to a.


                                                        

 

8. Change the order of integration and hence evaluate

Solution: We have

           

  

By changing the order of integrations we get;