Derivatives and Integrals Practice for grunewald ap calculus Flashcards

1

\int_0^1x^2dx

\frac{1}{\sqrt{2}}
\frac{\pi}{4}
\frac{1}{3}
\frac{1}{2}

2

\frac{d}{dx}\left(\arcsin x\right)

\frac{1}{1+x^2}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1-x^2}
\arccos x

3

\int_{ }^{ }\left(1+x\right)dx

x+\frac{x^2}{2}+C
1+\frac{x^2}{2}
x+\frac{x^2}{2}
1

4

\int_{ }^{ }\frac{1}{1+x^2}dx

\arctan x+C
\operatorname{arcsec}x+C
\ln\left|1+x^2\right|+C
\frac{\ln\left|1+x^2\right|}{2x}

5

\int_{ }^{ }\left(\tan x\right)dx

\ln\left|\csc x\right|
-\ln\left|\cos x\right|+C
\sec^2x+C
\frac{\tan^2\left(x\right)}{2}+C

6

\int_1^∞\frac{1}{x}dx

-1
\frac{1}{2}
1
diverges

7

\int_{ }^{ }\cos^2\left(x\right)dx

\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)+C
\frac{1}{\csc^2x}+C
\frac{\ln\left|\cos^3\left(x\right)\right|}{3}+C
not integrable

8

\frac{d}{dx}\left(4^x\right)

4e^x
\ln4\cdot4^x
\frac{1}{\ln4}4^x
\frac{\left(4^x\right)^2}{e^x}

9

\int_{ }^{ }\left(\ln x\right)dx

not integrable
\frac{\ln\left(x\right)^2}{2}-x+C
x\ln x-x+C
\frac{1}{x}+C

10

\frac{d}{dx}\left(\left(1+\cos\left(x^2\right)\right)\cdot e^x\right)

e^x\left(1+\cos\left(x^2\right)+2x\sin\left(x^2\right)\right)
e^x\left(-2\sin\left(x^2\right)+2x\cos\left(x^2\right)\right)
e^x\left(1+\cos\left(x^2\right)-2x\cdot\sin\left(x^2\right)\right)
e^x\left(-2x\sin\left(x^2\right)+\cos\left(x^2\right)\right)

11

\int_{ }^{ }\cos\left(x\right)dx

-\sin\left(x\right)
\cos\left(x\right)
\sin\left(x\right)
\sin\left(x\right)+C

12

\frac{d}{dx}\left(x^2\right)

2x
underivable
\frac{x^3}{3}
2x^2

13

\int_{ }^{ }\left(x\tan x\sec^2x\right)dx

\frac{x\tan^2x}{2}-\frac{\tan x}{2}+\frac{x}{2}+C
\frac{x\tan^2x}{2}-\frac{\tan x}{2}-\frac{x}{2}+C
\frac{x\sec^2x}{2}-\frac{\tan x}{4}+\frac{x}{2}+C
\frac{x\sec^2x}{2}+\frac{\tan x}{2}-\frac{x}{4}+C

14

\frac{d}{dx}\left(e^2\right)

0
\frac{1}{2}e^2
e^2
2e^2

15

\frac{d}{dx}\left(e^x\right)

e^x+C
e^x

16

\int_{ }^{ }\frac{1}{x\ln\left(x^2\right)}dx

\frac{1}{2x\ln\left|x^2\right|}+C
\left(\ln\left|\ln\left|x^2\right|\right|\right)^2+C
\frac{1}{2}\ln\left|\ln\left|x\right|\right|+C
not integrable b/c one isn't derivative of the other

17

\int_{ }^{ }f\left(x\right)dx

f^{-1}\left(x\right)+C
F\left(x\right)+C
f^{-1}\left(x\right)
F\left(x\right)

18

\frac{d}{dx}\left(x\right)

x
1
\frac{x^2}{2}
1+C

19

\frac{d}{dx}\left(\sqrt{x}\right)

\frac{2}{3}x^{\frac{3}{2}}+C
\frac{1}{2\sqrt{x}}
-\frac{1}{2}\sqrt{x}
\frac{x^{\frac{1}{2}}}{2}

Derivatives and Integrals Practice for grunewald ap calculus

Questions 19

Derivatives and Integrals Practice for grunewald ap calculus

Questions 19