Test: Integration III - Challenging

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Question 1:   Solve integral ( 5 cos( x ) )d( cos( x ) )
F( x )= 5 cos( x ) +C
F( x )=5cos( x )+C
F( x )= 5 cos( x ) ln( 5 )
F( x )= 5 cos( x ) ln( 5 ) +C
Question 2:   Find the antiderivative of the function f( x )= cos 2 ( 7x )
F( x )= 1 2 ( x+ 1 14 ×sin( 14x ) )+C
F( x )= 1 2 ( x+sin( x ) )+C
F( x )= 1 2 ( x+sin( 14x ) )+C
F( x )=x+ 1 14 ×sin( 14x )+C
Question 3:   Find the antiderivative of the function f( x )= 8 1+9 x 2
F( x )=8arctan( 3x )+C
F( x )= 8 3 arctan( x 3 )+C
F( x )= 1 3 arctan( 3x )+C
F( x )= 8 3 arctan( 3x )+C
Question 4:   Calculate 0 π ( 1 cos 2 ( x 4 ) )dx
π
5
-3
4
Question 5:   Find the antiderivative of the function f( x )=5x+1 that passes via point ( 2;5 )
F( x )= 5 x 2 2 +x-3
F( x )= 5 x 2 2 +x
F( x )= 5 x 2 2 +x-7
F( x )= 5 x 2 2 +x+7
Question 6:   Find the antiderivative of the function f( x )= 7 x +2 that passes via point ( 0;0 )
F( x )= 7 x ln( 7 ) +2x+ 3 ln( 7 )
F( x )= 7 x ln( 7 ) +x- 1 ln( 7 )
F( x )= 7 x ln( 7 ) +2x- 1 ln( 7 )
F( x )= 7 x ln( 7 ) +2x+ 1 ln( 7 )
Question 7:   Calculate the area of the figure defined by y= cos( x ) ,x=0,x= π 6
5π 2
π 2
1 2
2π
Question 8:   Find the formula for the area of the shaded region:

S= 0 4 | x |dx
S= 0 2 ( x )dx
S=- 0 4 ( x )dx
S= 0 4 ( x )dx
Question 9:   Calculate the area of the figure defined by y= x 2 and y=x
1 6
1 4
1
6
Question 10:   Calculate the area of the figure defined by y=x , x=5 and y=0
13.5
12
12.5
10