Stack #41271
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| Meaning of definite integral | the limit of a Riemann sum; the integral from a to b of f(x)dx = sum from i=1 to n of f(x*)deltax where x* is a particular point in each subinterval and delta x is the length of the subinterval
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| Fundamental Theorem of Calculus | If f is continuous on [a,b] and F'=f, then the integral from a to b of f(x)dx=F(b)-F(a)
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| Integration by parts | integral of uv' = uv - integral of u'v
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| Volume of known cross-section | Integral from a to be of A(x)dx, where A(x) is the area of a cross-section
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| Volume using disks | integral from a to b of pi*r^2dx, where r is in terms of x
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| Volume using washers | integral from a to b of (pi*R^2-pi*r^2)dx, where R and r are in terms of x
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| Volume using cylindrical shells | integral from a to be of 2rpihdx, where r and h are in terms of x
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| Work | force=mass*acceleration; work=force*distance; work=volume of slice*density*distance
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| Limit comparison test | positive terms - if the limit as n goes to infinity of the terms of sequence a over sequence b = c, and c>0 and finite, then either both series diverge or both converge
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| Alternating series test | positive terms - if b sub n+1 < b sub n and the lim as n goes to infinity of b sub n = 0, then the series converges
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| Ratio test | Limit as n goes to infinity of the absolute value of a sub n+1 over a sub n = L. If L<1, series converges. If L>1, series diverges. If L=1, then test is inconclusive
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| p-series | 1/(n^p), convergent if p>1
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| Alternating series estimation theorem | absolute value of s - s sub n < b sub n+1
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Created by:
emilyrose
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