Edexcel IALGeneralGeneral Applications6 Marks
Use the substitution u = x^2 to find ∫ (x / (√(1 - x^4))) dx
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for du/dx = 2x or dx = du/(2x)
- A1 for replacing x dx with 1/2 du and x^4 with u^2 (or equivalent in x if they do not change x dx) to get ∫ (1 / (√(1 - u^2))) (1/2) du
- A1 for correctly integrating 1/(√(1 - u^2)) to arcsin u (or sin⁻¹ u)
- M1 for multiplying by 1/2
- A1 for 1/2 arcsin(x^2) or 1/2 sin⁻¹(x^2)
- B1 for +c (independent mark, can be awarded if other marks are lost)
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