Mathematics Pure WMA11: Integration Topical Past Paper Questions

Figure 3 The curve C, shown in Figure 3, has parametric equations $$ x=6\sin t\quad y=5\sin2t\quad0\leqslant t\leqslant k $$ where k is a constant. The region R, also shown in Figure 3, is bounded by C and the x-axis. This region is rotated through $ 2\pi $ radians about the x-ax…

Figure 1 Figure 2 Figure 1 shows a sketch of part of the curve C with equation $$ y=\cos x+\frac{1}{5}\mathrm{e}^{x} $$ The finite region, shown shaded in Figure 1, is bounded by C, the y-axis, the x-axis and the line with equation x = 4 The region is rotated through $ 2\pi $ rad…

Figure 3 The curve C, shown in Figure 3, has equation $$ y=\frac{x^{-\frac{1}{4}}}{\sqrt{1+x}\left(\arctan\sqrt{x}\right)} $$ The region R, shown shaded in Figure 3, is bounded by C, the line with equation x = 3, the x-axis and the line with equation $ x = \frac{1}{3} $ The regio…