Find ∫√2x - 1 dx.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B2] (2x-1)^(3/2) / 3 [+c] oe isw (B1 for k × (2x-1)^(3/2) / (3/2) where k ≠ 0 or for (2x-1)^(3/2) / (3/2) × k where k ≠ 0)
2. [M1] for k cos 4x [+c] where k < 0 or k = -1/4
3. [A1] -1/4 cos 4x [+c]
4. [M1] Sight of correct substitution of limits: -1/4 cos(4π/4) - (-1/4 cos(4π/8)) oe; FT their k cos 4x from (b)(i); dep on M1 awarded in (b)(i)
5. [A1] 1/4
6. [M1] For integration leading to k e^(x/3) [+c] (implies k e^(x/3) with k any non-zero constant)
7. [A1] k = 3
8. [M1] Sight of correct substitution of limits: their k e^(ln8/3) - their k e^0 oe
9. [B1] Correct evaluation of e^(ln8/3) as 2
10. [A1] 6 - 3 = 3