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3.7 Integration (A-level only)

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Question 20

Figure 1 below shows the curve y=xln⁡xy = 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.

Figure for question 5

You may use the formula ∫udvdx dx=uv−∫vdudx dx\displaystyle\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx∫udxdv​dx=uv−∫vdxdu​dx.

Show that the exact area of R R\,R is Aln⁡2+BA\ln 2 + BAln2+B, where A A\,A and B B\,B are rational numbers to be found.

[7]
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3.7 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Integration (A-level only)

221 exam-style questions on WJEC A Level Maths 3.7 Integration (A-level only), covering 3.7.1 Integration (A-level only), 3.7.2 Integration (A-level only), 3.7.3 Integration (A-level only), 3.7.4 Integration (A-level only), 3.7.5 Integration (A-level only), and 3.7.6 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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