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no 5. a. ∫(2x -1) dx
0
1 1 1
∫(2x -1) dx = ∫2x dx -∫1 dx
0 0 0
1 1
∫(2x -1) dx = {(2/(1+1))x^(1+1) - 1x^(0+1)} ]
0 0
1 1
∫(2x -1) dx = (x^2 - x ) ]
0 0
1
∫(2x -1) dx =((1)^2 - (1)) - ( (0)^2 - (0) )
0
1
∫(2x -1) dx =0 - 0 = 0
0
4 4
b. ∫√x dx = ∫x^(1/2) dx
1 1
4 4
∫√x dx = 1/(1+1/2)x^(1/2+1) ]
1 1
4 4
∫√x dx = (2/3)x^(3/2 ]
1 1
4
∫√x dx = (2/3)(4)^(3/2) - (2/3)(1)^(3/2)
1
4
∫√x dx = 16/3 - 2/3 = 14/3
1