Additional Mathematics 0606: INTEGRATION Topical Past Paper Questions

(a) Differentiate $ x \sin(2x-3) $ with respect to x. [2] (b) Hence find $ \int_{0}^{\frac{1}{2}} x \cos(2x-3) \, dx $. [4]

(a) Integrate the following with respect to x. (i) $ e^{5x-2} $ [2] (ii) $ \frac{1}{4-3x} $ where $ x < \frac{4}{3} $ [2] (b) Show that $ \int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \sec^2\left(\frac{1}{2}x\right) dx = 2\left(1 - \frac{\sqrt{3}}{3}\right) $. [3]

Find the exact area of the region enclosed by the curve $ y = e^{2-4x} $, the x-axis, the line x = -0.25 and the line x = 0.5. [4]