Find ∫e^(4x+3) dx.

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

1. [M1] k e^(4x+3) (+c) oe any constant, non-zero k
2. [A1] (1/4) e^(4x+3) oe
3. [DM1] (1/4)(e^(4(3)+3) - e^(4(2.5)+3)) or better ft their integral attempt
4. [A1] 706 650.99... = 707 000 to 3 sf or better Accept (1/4)(e¹⁵-e¹³)
5. [M1] k sin(x/3) (+c) any constant, non-zero k
6. [A1] 3 sin(x/3)
7. [DM1] 3 sin(π/18) - 3sin(0) Dep on their integral attempt in sin; condone omission of lower limit
8. [A1] 0.520944... = 0.521 to 3 sf or better Accept 3 sin(π/18)
9. [B1] Expands - accept unsimplified
10. [M1] integration of their 3 term expansion
11. [A1] Fully correct
12. [B1] +c