Test: Integration II - Ambitious

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Question 1:   Find the antiderivative of the function f( x )= ( 2x+5 ) 2
F( x )= x 3 3 +5 x 2 +25x+C
F( x )= 4 x 3 3 +5 x 2 +25x+C
F( x )= 4 x 3 3 +5 x 2 +25x
F( x )= x 3 3 + x 2 2 +25+C
Question 2:   Find the antiderivative of the function f( x )= ( 2 6x ) 2
F( x )= 2 12x 12ln( 2 ) +C
F( x )= 2 12x ln( 2 ) +C
F( x )= 2 12x 12ln( 2 )
F( x )= 2 12x +C
Question 3:   Find the antiderivative of the function f( x )= 1 cos 2 ( 2x )
F( x )=tan( 2x )+C
F( x )= 1 2 tan( x )+C
F( x )= 1 2 tan( 2x )+C
F( x )= 1 2 tan( 2x )
Question 4:   Find the equation of integral for the area of the shaded region:

S= ( x 2 )dx
S= ( x 2 -( x+1 ) )dx
S= ( x+1 )dx
S= ( ( x+1 )- x 2 )dx
Question 5:   Find the antiderivative of the function f( x )= 1 21+ x 2
F( x )= 1 21 arctan( x 21 )+C
F( x )= 1 21 arctan( x 21 )
F( x )=arctan( x 21 )+C
F( x )= 1 21 arctan( x )+C
Question 6:   Calculate π 2π ( -sin( x 3 ) )dx
0
1
-3
- 1 3
Question 7:   Calculate 0 3 ( ( 4 9 x ) 2 -2 )dx
- 38 3
5
38 9
- 38 9
Question 8:   Calculate 0 1 ( 5 x +1 )dx
-1
5 ln( 5 ) -1
4 ln( 5 ) -1
ln( 5 )
Question 9:   Calculate the area of the figure defined by y= x 2 and y=1
4 3
3 4
1
2
Question 10:   Calculate the area of the figure defined by y=2x , x=2 and y=0
-4
5
2
4