Applications of Integration unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Cross-section area formulas
Total distance from a velocity function
Volume by disks and washers
Amount equals initial plus change
Horizontal slices mean right minus left
Volume by known cross sections
Upper curve can switch
Test which curve is on top
Average value divides by the width
Choosing dx or dy
Switch variables before splitting
Displacement vs total distance
Short answer 1. Define or explain: Area between two curves
3 ptsShort answer 2. Define or explain: In minus out
3 ptsShort answer 3. Define or explain: MVT for integrals
3 ptsShort answer 4. Define or explain: Arc length of y = f(x)
3 ptsFree response
9 ptsNO CALCULATOR. Let f be the function defined by f(x) = ∛(x − 1), and let g be the function defined by g(x) = e^(−2x + 4). The graphs of f and g intersect at the point (2, 1). Let R be the region bounded by the graph of f, the x-axis, and the vertical line x = 2, as shown in the figure (R lies between x = 1 and x = 2, under the graph of f).
A. Evaluate ∫₁² f(x) dx. Show the work that leads to your answer.
B. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid generated when region R is rotated about the x-axis.
C. Write, but do not evaluate, an expression involving one or more integrals that gives the perimeter of region R.
D. Evaluate ∫₂^∞ g(x) dx. Show the work that leads to your answer.