Skip to content

Course home

Sign up

1.11 H: Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114
Question 100

The profile of a specialized aerodynamic sail is modeled by a curve with parametric equations

x=36−6t,y=t336+6t,0≤t≤6 x = \sqrt{36-6t}, \quad y = \frac{t^3}{\sqrt{36+6t}}, \quad 0 \le t \le 6 x=36−6t​,y=36+6t​t3​,0≤t≤6

The curve intersects the yyy-axis at the point where t=6t=6t=6 and the xxx-axis at the point where t=0t=0t=0. The region RRR is bounded by the curve and the positive xxx and yyy axes.

a.

Show that the area of RRR is given by

K∫06t31296−36t2 dt K \int_{0}^{6} \frac{t^3}{\sqrt{1296-36t^2}} \, dt K∫06​1296−36t2​t3​dt

where KKK is a constant to be found.

[4]
b.

Using the substitution u=1296−36t2u = 1296 - 36t^2u=1296−36t2, or otherwise, find the exact area of RRR.

[7]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank