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AP Calculus Integrals and Derivatives Flashcards | StudBud
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AP Calculus Integrals and Derivatives
AP Calculus Integrals and Derivatives
20 terms
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A #mathreview for #calculus students in #integrals and #derivatives
Flashcards
20 cards
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Practice quiz
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Questions
20
Answers
1
∫sin
5
(2x)cos(2x)dx=
sin62x/6+C
sin62x/12+C
cos52x/3+C
sin62x/3+C
2
∫(2x
3
+5x+1)e
2x
dx
e2x (x3−3/2x2+4x−3/2)+C
e2x (x4−3/2x3+4x2−3/2x)+C
e2x (x3−3/2x2+4/2x−3/2)+C
ex (x3−3/2x+4x−3/2)+C
3
Solve the following integral: ∫(5x
2
-8x+5)dx
(5x3/2)-4x2+5x+C
(5x3/2)-x2+5x+C
(5x3/3)-4x2+5x+C
(5x3/3)-x2+5x+C
4
Solve the following integral: ∫(x
3/2
+2x+3)dx
(3/2x1/2/5)+2x2+3x+C
(2x5/2/5)+2x2+3x+C
(2x5/2/5)+x2+3x+C
(3/2x1/2/5)+x2+3x+C
5
Solve the derivative: y=cos
3
(√x)
y'=3sin2√xcos√x/2√x
y'=-3cos2√xsin√x/2√x
y'=-3sin2√xcos√x/2x
y'=3cos2√xsin√x/2x
6
Calculate the derivative of the function f(x) = cos(x
3
+ x
2
+ 1)
-(3x2 + 2x)sin(x4 + x3 + 1)
(3x2 + 2x)-sin(x3 + x2 + 1)
-(3x2 + 2x)sin(x3 + x2 + 1)
-(3x2 + 2x)cos(x3 + x2 + 1)
7
Solve the following definite integral (calculator active)
2.344
2.345
2.346
2.343
8
∫lnx/3xdx=
1/6ln2|x|+C
1/6ln2(ln|x|)+C
1/3ln|x|+C
1/3ln2|x|+C
9
Differentiate g(t)=(4t
2
-3t+2)
-2(8t-3)(4t2-3t+2)3
2(8t-3)(4t2-3t+2)3
2(8t-3)(4t2-3t+2)-3
-2(8t-3)(4t2-3t+2)-3
10
Find the derivative: y =√sin(x)
y'=sinx/2√cosx
y'=sinx/2cosx
y'=-cosx/2√sinx
y'=cosx/2√sinx
11
Find the first derivative of the inverse trig function: y=sin
-1
dy/dx=1/4x-x2
dy/dx=1/2cosy
dy/dx=1/√4x-x3
dy/dx=1/√4-x2
12
Evaluate the limit of the function using L'Hospital's Rule.
-6/5
6/5
5/6
-5/6
13
Solve the derivative: f (x) = 4x
3
− 3x
2
+ 2x – π
f'(x) = 12x2 − 6x + 2
f'(x) = 4x3/3 − 6x + 2
f'(x) = 12x3 − 6x2 + 2
f'(x) = 12x2 − 6x + 2-π
14
∫sin
4
xdx
-1/4(3x2/2−sin2x+1/8sin4x)+C
1/4(3x3/3−sin22x+1/8sin4x)+C
1/4(3x/2−cos2x+1/8sin4x)+C
1/4(3x/2−sin2x+1/8sin4x)+C
15
Solve the following integral: ∫5cos(Θ)dΘ
5cos(Θ)sin(Θ)+C
-5sin(Θ)+C
5sin(Θ)+C
-5cos(Θ)+C
16
Find ∫e
1/x
/x
3
dx.
e1/x/ x2 + ex + C
e1/x/ x2 + 2e1/x + C
−e1/x/ 2x + ex + C
−e1/x/ x + e1/x + C
17
Find ∫3x
2
arctanx
3
dx
(t)arctan(t)2−1/2ln(1+t2)+C
t+arctan(t)−1/2ln(1+t2)+C
(t)arctan(t)−1/2ln(1+t2)+C
t+arctan(t)2−1/2ln(1+t2)+C
18
Find the derivative: y=e
x
/x
y'=(ex/x)-(ex/x2)
y'=(ex/x)-(e2/x2)
y'=(ex/x2)-(e2x/x2)
y'=(e2x/x)-(ex/x2)
19
The average value of f(x)=1/x from x=1 to x=e is
1/(1-3)
1/(e-1)
1/(e+1)
e-1
20
Solve the derivative: f (x) = (3x-2)(2x+1)
f '(x) = 6x −1
f '(x) = 12x −1
f '(x) = 12x +1
f '(x) = 12x −x-2
