Test: Integration II - Challenging

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Question 1:   Solve integral ( 1 cos 2 ( e x ) )d( e x )
F( x )=tan( e x )
F( x )= e x +C
F( x )=tan( e x )+C
F( x )=tan(x)+C
Question 2:   Find the antiderivative of the function f( x )= cos 2 ( 3x )
F( x )= 1 2 ( x+ 1 6 ×sin( 6x ) )+C
F( x )= 1 2 ( x+sin( 6x ) )+C
F( x )= 1 2 ( x+sin( x ) )+C
F( x )=x+ 1 6 ×sin( 6x )+C
Question 3:   Find the antiderivative of the function f( x )= 5 1+16 x 2
F( x )=5arctan( 4x )+C
F( x )= 1 4 arctan( 4x )+C
F( x )= 4 5 arctan( 4x )+C
F( x )= 5 4 arctan( 4x )+C
Question 4:   Calculate 0 π ( sin( x 3 ) )dx
3.5
1.5
1
π
Question 5:   Find the antiderivative of the function f( x )=9 x 2 -x that passes via point ( 1;1 )
F( x )=3 x 3 - x 2 2 +C
F( x )=3 x 3 - x 2 2 -1
F( x )=3 x 3 - x 2 2 +2
F( x )=3 x 3 - x 2 2 -1.5
Question 6:   Find the antiderivative of the function f( x )=sin( x )+cos( x ) that passes via point ( π;0 )
F( x )=-cos( x )+sin( x )+C
F( x )=-cos( x )+sin( x )+1
F( x )=-cos( x )+sin( x )
F( x )=-cos( x )+sin( x )-1
Question 7:   Calculate the area of the figure defined by y=x,x=3,x=9.
225π
234π
81π
729π
Question 8:   Find the formula for the area of the shaded region:

S=- 0 2π ( cos( x ) )dx
S= 0 π ( cos( x ) )dx
S= 0 π 2 ( cos( x ) )dx - π 2 3π 2 ( cos( x ) )dx + 3π 2 2π ( cos( x ) )dx
S= 0 2π ( cos( x ) )dx
Question 9:   Calculate the area of the figure defined by y= x 2 and y=2x
4 3
3 4
1
4
Question 10:   Calculate the area of the figure defined by y=3x , x=2 and y=0
4
2
6
7