Math 106: Review for Final Exam, Part I
1. Find the following. [See Review for Exam II for integration tips and strategies.]
(a) Z12x2cos(x3)dx
(b) Z∞
0
xe−3xdx
(c) Z6
0
dx
(x−4)2
(d) Z3x2+2x−5
(x2+ 1)(x−4) dx
(e) Zπ/3
0
tan3xsec5xdx
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Ordered - Calculus - Exam, Exams of Calculus
Some keywords from this exam paper are: Ordered, Integration Tips, Strategies, Possible Left, Approximations, Data, Numerical Integration, Estimate, Certainty, Errors
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2012/2013
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Math 106: Review for Final Exam, Part I
- Find the following. [See Review for Exam II for integration tips and strategies.]
(a)
12 x^2 cos(x^3 ) dx
(b)
0
xe−^3 x^ dx
(c)
0
dx (x − 4)^2
(d)
3 x^2 + 2x − 5 (x^2 + 1)(x − 4)
dx
(e)
∫ (^) π/ 3
0
tan^3 x sec^5 x dx
(f)
25 − x^2 dx
- Find the best possible left, right, midpoint, trapezoidal, and Simpson’s approximations to
− 2
f(x) dx given the data in the table below. [8:00 and 9:30 sections may omit Simpson’s approximation.]
x -2 -1.5 -1 -0.5 0 f(x) 2 3 6 10 11
- If you use numerical integration to estimate
∫ (^) b a ln^ x dx, how would the following be ordered from least to greatest? L 100 , R 100 , M 100 , T 100 , S 200. [8:00 and 9:30 sections may omit S 200 .]
What can you say with certainty about where
∫ (^) b a ln^ x dx^ would fit into your ordering?
- Consider the region bounded by y = 0, x = 2, and y = x^2. Write an integral equal to the volume of the object created when the region is revolved about
(a) the x-axis
(b) the line x = 5
- A spherical tank of radius 8 feet is buried 5 feet below ground and filled to a height of 11 feet with gasoline (42 pounds per cubic foot). Write an integral equal to the work done in pumping all the gasoline to ground level.
- Find the solution to
dy dx
cos x y^2
that passes through (0, 2).