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Inverse trig derivatives and integrals Flashcards | StudBud
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Inverse trig derivatives and integrals
Inverse trig derivatives and integrals
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A #calculus review of the derivatives of #trigonometric and #inverse trigonometric functions
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Answers
1
sin
-1
(sin 5π/4 )=
5π/4
π/4
√(½)
-π/4
2
∫ sec x dx
ln |sec x + tan x| +c
-ln |cos x| +c
-ln |sec x + tan x| +c
secxtanx + c
3
\frac{d}{dx}\sec^{-1}x=
\frac{1}{1+x^2}
\frac{1}{\left|x\right|\sqrt{x^2-1}}
\frac{-1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
4
Which differential equation would produce this slope field?
\frac{dy}{dx}=xy
\frac{dy}{dx}=x-y
\frac{dy}{dx}=2x
\frac{dy}{dx}=x+y
5
\int_{ }^{ }\frac{dx}{\sqrt{x}}=
\sqrt{x}+c
Arc tan (x)+c
ln |x|+c
2\sqrt{x}+c
6
\frac{d}{dx}\sin^{-1}x=
\frac{-1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
\frac{1}{\left|x\right|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
7
\frac{d}{dx}\left(\cot^{-1}x\right)=
\frac{1}{1+x^2}^{ }
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{1+x^2}
\frac{1}{\left|x\right|\sqrt{1-x^2}}
8
\int_{ }^{ }\frac{1}{\sqrt{a^2-u^2}}du
\sin^{-1}u+c^{ }
\frac{1}{a}\sin^{-1}\left(\frac{u}{a}\right)+c
\cos^{-1}\left(\frac{u}{a}\right)+c
\sin^{-1}\left(\frac{u}{a}\right)+c
9
\int_{ }^{ }\frac{dx}{a^2+x^2}=
\frac{1}{a}\tan^{-1}(\frac{x}{a})+c
\ln\left(a^2+x^2\right)+c
\tan^{-1}(\frac{x}{a})+c
\frac{1}{a}\tan^{-1}(x)+c
10
\frac{d}{dx}\left(\csc x\right)=
cotx
-cscxcotx
tanx
-csc2x
11
\frac{d}{dx}\tan^{-1}x=
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
\frac{1}{\left|x\right|\sqrt{x^2-1}}
12
\int_{ }^{ }a^xdx
a^x\ln a+c
x\ln a+c
a^x+c
\frac{a^x}{\ln a}+c
13
\int_{ }^{ }\frac{dx}{x\sqrt{x^2-a^2}}=
\frac{1}{a}\sec^{-1}\left(\frac{\left|x\right|}{a}\right)+c
\sec^{-1}\left(\frac{\left|x\right|}{a}\right)+c
\frac{1}{a}\sec^{-1}\left(\frac{x}{a}\right)+c
\frac{1}{a}\sin^{-1}\left(\frac{x}{a}\right)+c
14
∫ tan x dx
ln |tan x + sec x| +c
-ln |sin x| +c
ln |cos x| +c
-ln |cos x| +c
15
\frac{d}{dx}[3^{\sin x}]=
3^{\sin x}\cos x
3^{\sin x}
3^{\sin x}(\ln3)\cos x
3^{\sin x}(\ln3)
