MATH1013 Test 2
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1
$\int_{}^{}\text{tanxdx}$
-ln|cosx| + c
2
$\int_{}^{}\text{cotxdx}$
ln|sinx| + c
3
$\int_{}^{}\text{secxdx}$
ln|secx + tanx| + c
4
$\int_{}^{}\text{cscxdx}$
-ln|cscx + cotx| + c
5
$\int_{}^{}\mathrm{sec}_{}^{2}\text{xdx}$
tanx + c
6
$\int_{}^{}\mathrm{csc}_{}^{2}\text{xdx}$
-cotx + c
7
integration by parts formula
$\int_{}^{}\text{udv} = \text{uv}-\int_{}^{}\text{vdu}$
8
trig substiutions (9 of them)
9
improper integrals (infinite) for the following (how to change them)
10
improper integrals (discont) for the following (how to change them)
11
area under a curve f(x) on [a,b]
$A=\int_{a}^{b}f(x)dx$
12
area between non-intersecting curves g(x) and f(x) where g(x)>f(x) on [a,b]
$A=\int_{a}^{b}[g(x)-f(x)]dx$
13
area between intersecting curves where g(x)>f(x) on [a,c] amd f(x)>g(x) on [c,b]
$A=\int_{a}^{c}[g(x)-f(x)]dx - \int_{c}^{b}[f(x)-g(x)]dx$