Mathematics 7356: Integration Topical Past Paper Questions

A curve has equation $$ y=x-a\sqrt{x}+b $$ where $a$ and $b$ are constants. The curve intersects the line y = 2 at points with coordinates $ (1, 2) $ and $ (9, 2) $, as shown in the diagram below. (a) Show that $a$ has the value 4 and find the value of $b$ (b) On the diagram, the…

(a) $ \text{Find } \int\left(2x^{3} + \frac{8}{x^{2}}\right) \, dx $ [3 marks] (b) A curve has gradient function $ \frac{dy}{dx} = 2x^3 + \frac{8}{x^2} $ The $ x $-intercept of the curve is at the point $ (2, 0) $ Find the equation of the curve. [2 marks]

The diagram below shows the graphs of $y = x^{2} - 4x - 12$ and $y = x + 2$ (a) Write down three inequalities which together describe the shaded region. vwrite down three inequalities which together describe the snaded region. [2 marks] Find the coordinates of the points A, B and…