Test: Integration I - Challenging

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Question 1:   Solve integral ( 1 1- sin 2 ( 3x ) )d( sin( 3x ) )
F( x )=sin( 3x )+C
F( x )=arcsin( sin( 3x ) )+C
F( x )=sin( arcsin( 3x ) )+C
F( x )=arcsin( sin( 3x ) )
Question 2:   Find the antiderivative of the function f( x )= sin 2 ( 5x )
F( x )= 1 2 ( x-sin( 10x ) )+C
F( x )=x- 1 10 ×sin( 10x )+C
F( x )= 1 2 ( x- 1 10 ×sin( 10x ) )+C
F( x )= sin 3 ( 5x ) 3 +C
Question 3:   Find the antiderivative of the function f( x )= 1 1+5 x 2
F( x )= 5 arccot( 5 x )+C
F( x )= 1 5 arccot( x )+C
F( x )=5arccot( 5 x )+C
F( x )= 1 5 arccot( 5 x )+C
Question 4:   Calculate 0 π ( cos( x 2 ) )dx
1
4
2
π
Question 5:   Find the antiderivative of the function f( x )=8 x 3 +3 x 2 that passes via point ( 1;5 )
F( x )=2 x 4 + x 3 +C
F( x )=2 x 4 + x 3
F( x )=2 x 4 + x 3 +2
F( x )=2 x 4 + x 3 +5
Question 6:   Find the antiderivative of the function f( x )= e x +3 hat passes via point ( 0;-7 )
F( x )= e x +3x+2
F( x )= e x +3x+C
F( x )= e x +3x+8
F( x )= e x +3x-8
Question 7:   Calculate the area of the figure defined by y= x ,x= 2 3 ,x= 8 3
2π
3π 10
10π 3
5π 3
Question 8:   Find the formula for the area of the shaded region:

S= 0 π ( sin( x ) ) dx
S= 0 π ( sin( x ) ) dx- π 2π ( sin( x ) ) dx
S=- 0 2π ( sin( x ) ) dx
S= 0 2π ( sin( x ) ) dx
Question 9:   Calculate the area of the figure defined by y= x 2 and y=3x
5
9
3
4.5
Question 10:   Calculate the area of the figure defined by y= x 2 , x=4 and y=0
6
7
2
4