IB Maths AA SL 5.11 Definite integrals and areas Question Bank

(f) EITHER

Attempt to form the required integral involving subtraction in either order.
$\int_{t_{1}}^{t_{2}}\left|L_{1}-f(x)\right| \mathrm{d} x$
correct expression with limits 1 and their x value at B
$\int_{1}^{1.64856 \ldots}\left|\left(\frac{1}{6} x+\frac{11}{6}\right)-\left(\frac{2}{\pi} \sin 3 \pi x+2\right)\right| \mathrm{d} x$ (or equivalent)

OR
intersection point between A and B is ( 1.34287 . . ., 2.05714 . .. )
subtracting $L_{1}$ and f, in either order, and substituting into area of region formula for one area with correct limits.

Two correct expressions OR correct values
$\int_{1}^{1.34287 \ldots}\left(\left(\frac{1}{6} x+\frac{11}{6}\right)-\left(\frac{2}{\pi} \sin 3 \pi x+2\right)\right) \mathrm{d} x=(0.144618 \ldots)$ AND
$\int_{1.34287 \ldots}^{1.64856 \ldots}\left(\left(\frac{2}{\pi} \sin 3 \pi x+2\right)-\left(\frac{1}{6} x+\frac{11}{6}\right)\right) \mathrm{d} x=(0.108585 \ldots)$

THEN
0.253204...
(area =) 0.253