IB Maths AA SL 5.11 Definite integrals & areas

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise setting up definite integrals for shaded regions, enclosed areas, accumulated motion and numerical approximations.

How this is tested

choose upper minus lower curves and correct limits to form one area integral or a difference of integrals
find enclosed areas with e^x, polynomials, or lines, using exact ln forms if needed
use definite integrals or accumulated distances from turning points to determine total distance travelled

[Maximum number: 5]

Consider the function defined by $f(x)=\frac{1}{2} x^{2}+k x+13$ , where $x \in \mathbb{R}$ and $k \in \mathbb{Z}^{+}$ .

Hence, find the shaded area.