Find ∫e^(4x+3) dx.
- (a)(i)Find ∫e^(4x+3) dx.[2]
- (a)(ii)Hence evaluate ∫[from 2.5 to 3] e^(4x+3) dx.[2]
- (b)(i)Find ∫cos(x/3) dx.[2]
- (b)(ii)Hence evaluate ∫[from 0 to π/6] cos(x/3) dx.[2]
- (c)Find ∫(x⁻¹ + x)² dx.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [M1] k e^(4x+3) (+c) oe any constant, non-zero k
- [A1] (1/4) e^(4x+3) oe
- [DM1] (1/4)(e^(4(3)+3) - e^(4(2.5)+3)) or better ft their integral attempt
- [A1] 706 650.99... = 707 000 to 3 sf or better Accept (1/4)(e¹⁵-e¹³)
- [M1] k sin(x/3) (+c) any constant, non-zero k
- [A1] 3 sin(x/3)
- [DM1] 3 sin(π/18) - 3sin(0) Dep on their integral attempt in sin; condone omission of lower limit
- [A1] 0.520944... = 0.521 to 3 sf or better Accept 3 sin(π/18)
- [B1] Expands - accept unsimplified
- [M1] integration of their 3 term expansion
- [A1] Fully correct
- [B1] +c
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