Find $\displaystyle\int(5-3\sqrt{x})^2\ \mathrm{d}x$.
$25x - 20x^{\frac{3}{2}} + \dfrac{9}{2}x^2 + c$
The speed, $v$ ms$^{-1}$, of a rollercoaster at time $t$ s is given by $$v(t) = \dfrac{1}{20}(50\sqrt{t} + 20t^2 - t^3)$$ Find the distance travelled by the rollercoaster at $20$ s, giving your answer to 3 significant figures.
$816$
The first few terms of an arithmetic sequence are $5, 9, 13, 17, 21, ...$ - Find the fortieth term of the sequence.
- Determine the sum of the first forty terms of the sequence.
Evaluate $$\sum_{r=1}^{20}(2r-3)$$
$360$
A geometric series has common ratio $\dfrac{1}{3}$ - Find the first term of the series, given that the sum of its first four terms is $36$.
- Determine the sum to infinity of the series.