MATH1013 Test 2

Question 1

$\int_{}^{}	ext{tanxdx}$

Accepted Answer

-ln|cosx| + c

Question 2

$\int_{}^{}	ext{cotxdx}$

Accepted Answer

ln|sinx| + c

Question 3

$\int_{}^{}	ext{secxdx}$

Accepted Answer

ln|secx + tanx| + c

Question 4

$\int_{}^{}	ext{cscxdx}$

Accepted Answer

-ln|cscx + cotx| + c

Question 5

$\int_{}^{}\mathrm{sec}_{}^{2}	ext{xdx}$

Accepted Answer

tanx + c

Question 6

$\int_{}^{}\mathrm{csc}_{}^{2}	ext{xdx}$

Accepted Answer

-cotx + c

Question 7

integration by parts formula

Accepted Answer

$\int_{}^{}	ext{udv} = 	ext{uv}-\int_{}^{}	ext{vdu}$

Question 8

area under a curve f(x) on [a,b]

Accepted Answer

$A=\int_{a}^{b}f(x)dx$

Question 9

area between non-intersecting curves g(x) and f(x) where g(x)>f(x) on [a,b]

Accepted Answer

$A=\int_{a}^{b}[g(x)-f(x)]dx$

Question 10

area between intersecting curves where g(x)>f(x) on [a,c] amd f(x)>g(x) on [c,b]

Accepted Answer

$A=\int_{a}^{c}[g(x)-f(x)]dx - \int_{c}^{b}[f(x)-g(x)]dx$

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