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Consider the following integral. Sketch its region of integration in the xy-plane.

$\displaystyle \int_{0}^{3} \int_{y^2}^{9} y\sin\!\left(x^{2}\right) \, dx \, dy$

(a) Which graph shows the region of integration in the xy-plane?

(b) Write the integral with the order of integration reversed:

$\displaystyle \int_{0}^{3} \int_{y^2}^{9} y\sin\!\left(x^{2}\right) \, dx \, dy = \int_{A}^{B} \!\! \int_{C}^{D} y\sin\!\left(x^{2}\right) \, dy \, dx$

with limits of integration

A =
B =
C =
D =

(c) Evaluate the integral.



A		B



C		D

(Click on a graph to enlarge it)