Answer:
a=0;b=9;c=0;d=√x
[tex]\int_0^3\int_{y^2}^{9}y\sin(x^2)dxdy=\int_{0}^{3}\int_{0}^{\sqrt{x}}y\sin(x^2)dydx[/tex]
Step-by-step explanation:
Given:
[tex]\int_0^3\int_{y^2}^{9}y\sin(x^2)dxdy=\int_{a}^{b}\int_{c}^{d}y\sin(x^2)dydx[/tex]
We need to change order of integration dxdy to dydx
[tex]0\leq y\leq 3;y^2\leq x\leq 9[/tex]
We have to change limit of x and y to change in order of integration
Please see the attachment for graph and order of integration.
[tex]0\leq x\leq 9;0\leq y\leq \sqrt{x}[/tex]
[tex]\int_0^3\int_{y^2}^{9}y\sin(x^2)dxdy=\int_{0}^{3}\int_{0}^{\sqrt{x}}y\sin(x^2)dydx[/tex]
Therefore,
a=0
b=9
c=0
d=√x
