Figure 1 below shows the curve y=xlnxy = x\ln xy=xlnx for x>0x > 0x>0. The region R R\,R is bounded by the curve, the line x=4x = 4x=4 and the xxx-axis.
You may use the formula ∫udvdx dx=uv−∫vdudx dx\displaystyle\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx∫udxdvdx=uv−∫vdxdudx.
Show that the exact area of R R\,R is Aln2+BA\ln 2 + BAln2+B, where A A\,A and B B\,B are rational numbers to be found.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.