Calculus II
Review for Exam 1
The following is a list of the sections and topics that may appear on the first exam. To determine
what you need to review in more detail, work through homework assignments without the aid of
notes. Study, and then rework those problems that caused difficulties. Perhaps, writing and
taking a “practice exam” will help overcome the anxiety associated with test taking.
Section 5.3
Evaluate derivatives of integral functions using the Fundamental Theorem of Calculus, Part 1
Evaluate definite integrals using the Fundamental Theorem of Calculus, Part 2
Section 5.4
Know the basic integration formulas. [Remember the “+ C” in every answer.]
Section 5.5
Evaluate indefinite and definite integrals using u-substitution [Notice the form of the answer
for each type.] Tips: Pick u as the inside of the messiest part. Don't forget du! Never write the
integral with x’s and u’s together. Remember to change limits, if needed.
Section 6.1
Find the area between two curves using either horizontal rectangles or vertical rectangles
Vertical rectangles:
dxfunction)(bottomfunction)(topArea
Horizontal rectangles:
dyfunction)(leftfunction)(rightArea
Section 6.2
Find the volume of a solid of revolution using the disk/washer method
Disk Method:
)(thicknessradiusVolume
2
Washer Method:
)(thicknessradius)(innerradius)(outerVolume
22
Remember that thickness of vertical rectangles is dx and the thickness of horizontal
rectangles is dy.
Remember to choose values for the upper and lower limits that match the variable.
Find the volume of a solid using known cross sections with area A
Perpendicular to the x-axis:
dxxA )(Volume
Perpendicular to the y-axis:
dyyA )(Volume
Section 6.3
Find the volume of a solid of revolution using the shell method
)(thickness(height)(radius)2Volume
Remember that thickness of vertical rectangles is dx and the thickness of horizontal
rectangles is dy.
Remember to choose values for the upper and lower limits that match the variable.