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Antiderivatives
∫(-x2+4x-3) dx : bounds 1 to 3
∫(x5-6x2+x-1) dx
Antiderivatives
50 terms
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An #antiderivative game that's #helpful
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Answers
1
∫(x
5
-6x
2
+x-1)
dx
(x6/6)
(x6/6)-2x3+(x2/2)-x+C
(x6/6)-2x3+C
(x6/6)-2x3+(x2/2)-2x+C
2
∫(-x
2
+4x-3) dx : bounds 1 to 3
16
22
(5/3)
0
3
What is the
integration formula
of ∫csc
2
x dx?
cotx+C
(1/csc2x)+C
cosx+C
-cotx+C
4
∫(x+1)/(√x) dx
(2/3)x3/2+2x1/2+c
(3/2)
3x3/2+2x1/2x+c
(2/3)x3/2+2x3/2+c
5
What is the anti-derivative of 2x
2x2
2
x3
x2
6
look at the picture below..
5/2
2
5
2/5
7
Is C needed if there are bounds?
no, not at all
no
yes, yes it does
yes
8
∫(sinx)/(cos
2
x) dx
secx+C
cosx+sinx+C
sin2x+C
cosx+C
9
∫(x
3
-4sinx)
dx
(x4/4)+5cosx+C
(x4/4)+4sinx+C
(x5/5)+4cosx+C
(x4/4)+4cosx+C
10
∫(sinx/(cosx+1))
dx
sinx+C
secx/cosx+1+C
sinx/cosx+1+C
cosx+1+C
11
∫x(x+1)
10
dx
(x+1)12/12-(x+1)11/11+C
(x+1)12-(x+1)11+C
(x+1)12/12-(x+2)11/11+C
(x+2)12/12-(x+1)11/11+C
12
What is this formula?
Mean Value Theorem
Average Value Theorem
Integral Formula
Average Value of a Function on an interval
13
∫√(2x-1) dx
3/2
(2x-1)3/2+C
(1/3)(2x-1)3/2+C
x+C
14
∫(1+x
3/2
)
4
dx
1/2(1+x3/2)5/15+C
2(1+x3/2)5/15+C
2(1+x3/2)+C
15
∫x
-3
dx
-3x-2
x-2/-2+c
(-1/2x2)+c
-3x-4
16
∫ (1/∛x)
dx
(x1/2/(1/2))+C
3x1/3+C
x1/3
(1/3x)+C
17
A differential equation in x and y is an equation that involves...
x and y
x, y, and derivatives of x
the derivative
x, y, and derivatives of y
18
∫x
5/2
dx
x7/2/(2/7)+C
(2/7)x7/2+C
x2/7/(7/2)+C
(7/2)x2/7+C
19
∫ (x+1)/(x)
dx
ln|x|+C
x+ln|2x|+C
x+ln|x|+C
x+ln|x1/2|+C
20
∫e
2x-5
dx
3/2e(2x-5)+C
1/2e(3x-6)+C
1/2e(2x-5)+C
2e(2x-5)+C
21
∫x
3
+x
2
+x
dx
(1/4)x4+(1/3)x3+(1/2)x2+C
(1/4)x4+(1/3)x3+(1/2)2+C
(1/4)x4+(1/3)x3+(3/2)x2+C
(3/4)x4+(1/3)x3+(1/2)x2+C
22
∫(t
2
+1)
2
dt
(1/5)t5+(2/3)t3+t
(1/5)t5+(2/3)t3+t+C
5t4+(2/3)t3+t+C
(1/5)t5+(2/3)t3+t+C
23
∫(√(x)+(1/x
3
)
dx
(2/3)x2/3 -(1/2x2)+C
(2/3)x3/2 -(1/2x2)+C
(2/3)x3/2 -x2+C
24
∫3x dx
3x2+c
3+c
(3/2)x+c
(3/2)x2 +c
25
∫(4cosx-cotx)
dx
4cosx-ln|sinx|+C
sinx-ln|sinx|+C
4sinx-ln|sinx|+C
26
∫ √x
dx
x2/3/(3/2)+C
(2/3)x3/2+C
x3/2/(2/3)+C
27
What is this sign used for?
Anti-derivative
Implicit differentiation
Limits
Derivative
28
∫x√x
dx
with bounds of 4 and 9
5
22
422/5
421/6
29
∫cost
dt
with bounds of 0 and x
cosx
cosx+sinx
1/sinx
sinx
30
∫(2/(√x)) dx
(1/2)4+C
4x1/2+C
4x1/2
(1/2)x4+C
31
∫csc
2
u du
(-1/2)sec(x2)+C
(1/2)cot(x2)+C
(-1/2)cot(x3)+C
(-1/2)cot(x2)+C
32
∫5
dx
5x
5
5+C
5x+C
33
∫(2x
2
-3x+2)
dx
bounds 0 to 2
2
3/10
3
10/3
34
What is the
integration formula
of ∫secxtanx dx?
secx+C
tanx+C
-secx+C
-tanx+C
35
∫
dx
2x+C
x+C
x3/2+C
x1/2+C
36
∫x √(x-2)
dx
(x-2)1/2+C
1/2(x-2)1/2
(x-2)3/2
(2x-2)1/2
37
∫x(x
2
+1)
2
dx
(1/6)(X2+1)3+C
(X2+1)3+C
6(X2+1)3+C
(X+1)3+C
38
∫xe
x^2
dx
(ex^2/2)+e+C
(ex^3/2)+C
(ex^2/2)+C
(2ex/2)+C
39
What is the
integration formula
of ∫0 dx?
C
(1/2)x+C
ABC
x2+C
40
∫ x(x
5
+1)
dx
(x8/8)+(x2/2)+C
(x2/2)+C
(x7/7)+C
(x7/7)+(x2/2)+C
41
∫x
3
dx
x4/4+C
3x2
x4/4
6x
42
∫(1/u)
du
: du= 1/x dx
ln/2|lnx|+C
ln|2lnx|+C
lnu+C
43
∫(9-x
2
)x
1/2
dx
6x2/3-(2x7/2/7)+C
5x3/2-(2x7/2/7)+C
6x3/2-(2x7/2/7)+C
44
∫tanu (2du)
-2ln|cos(x/2)|+C
2ln|cos(x/2)|+C
ln|cos(x/2)|+C
-ln|cos(x/2)|+C
45
∫x
3
dx
bounds 1 to 3
5
20
-10
10
46
C stands for...
calculus
constant
circle
circumference
47
∫(x
3
+3)/(x
2
)
dx
(1/2)x2-(3/x)+C
2x2+C
(4x3/2x)
(1/2)x2+C
48
∫(∛x)(x-4)
dx
7x4/3(x-7)+C
(3/7)x4/3(x-7)+C
(3/7)x4/3(x-7)2+C
3x4/3(x-7)+C
49
∫cos(x/2)
dx
with bounds of 0 & π
2
π/2
1
0
50
The definite integral as a number is...
∫f(x) dx with bounds a and b
∫f(x)3dx with bounds a and b
1/b-a ∫f(x) dx with bounds a and b
