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Date	November 2015	Marks available	4	Reference code	15N.1.hl.TZ0.2
Level	HL only	Paper	1	Time zone	TZ0
Command term	Find and Use	Question number	2	Adapted from	N/A

Question

Using integration by parts find $\int {x\sin x{\text{d}}x}$ .

Markscheme

attempt to integrate one factor and differentiate the other, leading to a sum of two terms M1

$\int {x\sin x{\text{d}}x = x( - \cos x) + } \int {\cos x{\text{d}}x}$ (A1)(A1)

$= - x\cos x + \sin x + c$ A1

Note: Only award final A1 if $+ {\text{ }}c$ is seen.

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 6 - Core: Calculus » 6.7 » Integration by parts.

17M.1.hl.TZ2.9b: Find $\int {f(x)\cos x{\text{d}}x}$ .
17M.1.hl.TZ1.9: Find $\int {\arcsin x\,{\text{d}}x}$
12M.1.hl.TZ2.10c: The region bounded by the graph, the x-axis and the y-axis is denoted by A and the region...
08M.1.hl.TZ2.6: Show that...
08N.1.hl.TZ0.5: Calculate the exact value of $\int_1^{\text{e}} {{x^2}\ln x{\text{d}}x}$ .
11M.2.hl.TZ2.13B: (a) Using integration by parts, show that...
11M.3ca.hl.TZ0.4a: Show that ${I_0} = \frac{1}{2}(1 + {{\text{e}}^{ - \pi }})$ .
SPNone.1.hl.TZ0.11b: Find the value of the integral $\int_0^{0.5} {\arcsin x {\text{d}}x}$ .
10M.1.hl.TZ2.9: Find the value of $\int_0^1 {t\ln (t + 1){\text{d}}t}$ .
13M.2.hl.TZ2.4a: Find $\int {x{{\sec }^2}x{\text{d}}x}$ .
15M.1.hl.TZ2.5: Show that $\int_1^2 {{x^3}\ln x{\text{d}}x = 4\ln 2 - \frac{{15}}{{16}}}$ .