Test: Integration I - Ambitious

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Question 1:   Find the antiderivative of the function f( x )= ( x-1 ) 2
F( x )= x 3 3 - x 2 +x+C
F( x )= x 3 3 - x 2 +x
F( x )= x 3 3 - x 2 2 +x+C
F( x )= x 3 3 +x+C
Question 2:   Find the antiderivative of the function f( x )= ( e x ) 2
F( x )= e 2x 2
F( x )= e 2x 2 +C
F( x )= e x 2 +C
F( x )= e 2x +C
Question 3:   Find the antiderivative of the function f( x )= 1 2x +4 x 3
F( x )= 1 2 ln| x |+ x 4 +C
F( x )= 1 2 ln| x |+ x 4 4 +C
F( x )= 1 2 ln| x |+ x 4
F( x )=ln| x |+ x 4 +C
Question 4:   Find the antiderivative of the function f( x )=2sin( x )+7cos( x )
F( x )=-2cos( x )+7sin( x )+C
F( x )=2cos( x )+7sin( x )+C
F( x )=-2cos( x )-7sin( x )+C
F( x )=-2cos( x )+7sin( x )
Question 5:   Find the antiderivative of the function f( x )= 1 16+ x 2
F( x )= 1 4 arctan( x 4 )+C
F( x )= 1 4 arctan( x )+C
F( x )= 1 4 arctan( x 4 )
F( x )= 1 2 arctan( x 2 )+C
Question 6:   Calculate 0 2π 3 ( cos( 3x 4 ) )dx
4 3
0
1
3 4
Question 7:   Calculate 0 5 ( ( 3 5 x ) 2 -5x )dx
-47.5
47.5
50.5
-50.5
Question 8:   Calculate 1 2 ( 2 x -3 )dx
-1
0
2 ln( 2 ) -3
2 ln( 2 )
Question 9:   Calculate the area of the figure defined by y= x 2 and y=4
1
4
32 3
3 32
Question 10:   Calculate the area of the figure defined by y=2x-4 , x=5 and y=0
3
25
9
12