f(x)=2x3−3x2+kx+2f(x) = 2x^3 - 3x^2 + kx + 2f(x)=2x3−3x2+kx+2, where k k\,k is a constant.
Given that (x+1)(x + 1)(x+1) is a factor of f(x)f(x)f(x), use the factor theorem to find the value of kkk.
Hence, showing all your working, write f(x)f(x)f(x) as a product of three linear factors.
The finite region R R\,R is bounded by the curve with equation y=f(x)y = f(x)y=f(x) and the xxx-axis, and lies below the xxx-axis. Find, using algebraic integration, the exact value of the area of RRR.
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.