Test: Integration III - Ambitious

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Question 1:   Find the antiderivative of the function f( x )= (x-3) 2
F( x )= x 3 3 -3 x 2 +9x+C
F( x )= x 3 -6 x 2 +9x+C
F( x )= x 3 3 -3 x 2 +C
F( x )= x 3 3 -3 x 2 +9x
Question 2:   Find the antiderivative of the function f( x )= e 6x
F( x )= e 6x 6
F( x )= e 6x 6 +C
F( x )=6 e 6x +C
F( x )= e x 6 +C
Question 3:   Find the antiderivative of the function f( x )=sin( 5x 3 )
F( x )=-cos( 5x 3 )+C
F( x )= 3 5 cos( 5x 3 )+C
F( x )=- 3 5 cos( 5x 3 )+C
F( x )=- 3 5 cos( 5x 3 )
Question 4:   Find the equation of integral for the area of the shaded region:

S= ( 3x-7x )dx
S= ( 3x+1 )dx
S= ( 3x-1 )dx
S= ( 3x )dx
Question 5:   Find the formula for the area of the shaded region:

S= ( 2 )dx
S= ( 2x-1 )dx
S= ( 7x+5 )dx
S= ( 2x )dx
Question 6:   Find the integral of the function f( x )= 1 7+ x 2
F( x )= 1 7 arctan( x 7 )
F( x )= 1 7 arctan( x )+C
F( x )= 1 7 arctan( x 7 )+C
F( x )= 7 arctan( x 7 )+C
Question 7:   Calculate 1 2 ( 4 x 3 +2x )dx
16
20
12
18
Question 8:   Calculate 0 2 ( x 2 +1 )dx
8
7
5
4
Question 9:   Calculate the area of the figure defined by y= x 2 and y=9
36
2
9
1 36
Question 10:   Calculate the area of the figure defined by y=x , x=5 and y=0
13.5
12.5
7
14