Question 34
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.
1.8 Integration Questions
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.