Mathematics AA: INTEGRATION Topical Past Paper Questions

[Maximum mark:29] The following question uses Maclaurin series to investigate approximations of mathematical constants and the accuracies of such approximations. (a) Given $ |x| [2] (b) Hence, use integration to show that the Maclaurin series of $ \arctan x $ may be expressed as…

[Maximum mark: 6] (a) Find $ \int\left(e^{4x}+6\right)dx $. It is given that $ h'(x) = e^{4x} + 6 $ and $ h(1.5) = 105 $.

[Maximum mark: 13] Consider the function $f$ defined by $f(x)=\frac{8x}{\left(x^{2}+1\right)^{3}}$, where $x\in\mathbb{R}$. The graph of $f$ is shown in the following diagram. (a) Show that $ f'(x)=\frac{8(1-5x^2)}{(x^2+1)^4} $. [A] (b) Find $\int f(x)dx$. [A] Consider a function…