{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2224Test2Review

# 2224Test2Review - MATH 2224 PRACTICE PROBLEMS FOR TEST#2 1...

This preview shows pages 1–2. Sign up to view the full content.

MATH 2224: PRACTICE PROBLEMS FOR TEST #2 1. Evaluate the following: a. dx dy x 1 0 x 3 0 2 ! ! b. ! ! " 2 0 y sin 0 x dy dx y cos e c. dy dx y 25 x 2 4 0 y 0 2 ! ! # d. ! ! ! # # # 6 0 x 6 0 z x 6 0 dx dz dy x 2. Reverse the order of integration and evaluate: ! ! + + 3 / 1 0 2 1 x 3 dx dy ) 3 x ( 3. Convert to rectangular coordinates and evaluate: ! ! " " \$ # \$ \$ 3 4 4 3 sec 5 0 2 3 d dr sin r 4. Find the area of the region bounded by the graphs of 1 y x 2 2 = + , 9 y x 2 2 = + using iterated integrals in polar coordinates. 5. Convert to polar coordinates and evaluate: dx dy y x 3 3 x 9 0 2 2 2 ! ! # # + 6. Graph the bounded region in the xy-plane and evaluate the integral ! ! ! # # # # 1 1 x 1 x 1 5 0 2 2 dx dy dz . 7. Find the volume of the region bounded by the graphs of 2 y x = , 2 y x 4 = # , z = 0, and z = 3. 8. Set up the triple integral in cylindrical coordinates to find the volume under 0 z y x = # + above the region in the fourth quadrant that lies outside r = 1 and inside \$ # = sin 1 r . Shade the proper region on the graph provided below. 9. Convert dA y x 4 R 2 2 !!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}