Integration
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Question 99
The sketch shows the curve y=x(x−2)(x−5)y = x(x - 2)(x - 5)y=x(x−2)(x−5)
a.[1]
Write down the values of x x\,x where the curve crosses the x x\,x axis.
b.[5]
Show that
∫02x(x−2)(x−5)dx=163 \int_0^2 x(x-2)(x-5) dx = \frac{16}{3} ∫02x(x−2)(x−5)dx=316and
∫25x(x−2)(x−5)dx=−634. \int_2^5 x(x-2)(x-5) dx = - \frac{63}{4}. ∫25x(x−2)(x−5)dx=−463.c.[3]
Hence find the area of the shaded region.
Integration Questions
411 exam-style questions on Edexcel A Level Maths Integration, covering 13.1 Integrating x^n, 13.2 Indefinite Integrals, 13.3 Finding Functions, 13.4 Definite Integrals, 13.5 Areas under Curves, 13.6 Areas under the x-axis, and 13.7 Areas between curves and lines. Each one has a worked solution and a mark scheme showing where the marks go.