WorksheetsIntegration by Substitution
Total questions: 12
Worksheet time: 20mins
Name
Class
Date
1.
∫ 6 x (x2 +1 )2 dx
a)
( x2 + 1)3 + C
b)
3 ( x2 + 1)3 + C
c)
( x2 + 1)1 + C
d)
6 ( x2 + 1)3 + C
2.
∫ 2x cos(x2) dx
a)
sin(x2) + C
b)
2 sin ( 2x ) + C
c)
(1/2) sin(x2) + C
d)
4 cos(2x ) + C
3.
a)
ln(2x2+6) + C
b)
ln(2x2+6)(4x) + C
c)
1/(2x2+6) + C
d)
1/(2x2+6)2 + C
4.
What should be used for u in the integral?
a)
no u needed
b)
4t2
c)
t3
d)
1/4t2
5.
What should be assigned to u in the integral?
a)
2x2
b)
sin (2x2)
c)
5x
d)
no u needed
6.
∫ 2 x (x2- 3)(1/2) dx
a)
(x2- 3)(3/2)+C
b)
(3/2)(x2- 3)(3/2)+C
c)
(2/3)(x2- 3)(3/2)+C
d)
(2/3)(x2- 3)(-1/2)+C
7.
∫ x (x2 + 7 )(1/3) dx
a)
(3/4) ( x2+ 7 )(4/3) + C
b)
(3/8) ( x2+ 7 )(4/3) + C
c)
( x2+ 7 )(4/3) + C
d)
(3/2) ( x2+ 7 )(4/3) + C
8.
∫ 2x cos(x2) dx
a)
sin(2x) + C
b)
2 sin ( 2x ) + C
c)
(1/2) sin(2x) + C
d)
4 cos(2x ) + C
9.
∫ g ' ( x ) f (u) dx, u = g ( x )
a)
∫ f ( u ) du
b)
g ( x ) + C
c)
( 1/ g ( x ) ) g ( x)4 + C
d)
cannot be determined
10.
∫(3x⁴+2)⁴(12x³)dx
a)
½(3x⁴+2)⁴+C
b)
(3x⁴+2)⁴+C
c)
⅕(3x⁴+2)⁵+C
d)
⅓(3x⁴+2)⁶+C
11.
Solve for u-substitution: ∫x(x²-2)15 dx
a)
((x²-2)¹⁶)/32 + C
b)
(x²-2)¹⁶ + C
c)
(x³-3)¹⁵ + C
12.
What is the choice of u for ∫ ex(1+ex)(1/2) dx?
a)
ex
b)
1+ex
c)
(1+ex)(1/2)
d)
(ex)(1/2)
100 %
