17M.1.AHL.TZ1.H_9

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt at integration by parts with $u=\arcsin x$ and $v^{\prime }=1$     M1

$\int \arcsin x\text{d}x=x\arcsin x-\int \frac{x}{\sqrt{1-x^2}}\text{d}x$    A1A1

 

Note:     Award A1 for $x\arcsin x$ and A1 for $-\int \frac{x}{\sqrt{1-x^2}}\text{d}x$.

 

solving $\int \frac{x}{\sqrt{1-x^2}}\text{d}x$ by substitution with $u=1-x^2$ or inspection     (M1)

$\int \arcsin x\text{d}x=x\arcsin x+\sqrt{1-x^2}+c$   A1

[5 marks]

[N/A]