2018 international practice exam ab mcq, part b - calculator required\n11 mark for review\nwhat is the…

Explanation:

Step1: Find the area formula of cross - section

The area of an isosceles right - triangle with leg length $l$ is $A=\frac{1}{2}l^{2}$. Here, the leg length $l$ of the isosceles right - triangle cross - section perpendicular to the $x$ - axis is $l = 4\cos(\frac{\pi x}{4})-(x - 2)^{2}$, so the area of the cross - section $A(x)=\frac{1}{2}[4\cos(\frac{\pi x}{4})-(x - 2)^{2}]^{2}$.

Step2: Set up the volume integral

The volume $V$ of the solid with cross - sectional area $A(x)$ from $x = 0$ to $x = 2$ is given by the definite integral $V=\int_{a}^{b}A(x)dx$. Here, $a = 0$, $b = 2$, so $V=\int_{0}^{2}\frac{1}{2}[4\cos(\frac{\pi x}{4})-(x - 2)^{2}]^{2}dx$.

Step3: Evaluate the integral using a calculator

Using a graphing calculator or a calculator with integral - evaluation capabilities, we input the integral $\int_{0}^{2}\frac{1}{2}[4\cos(\frac{\pi x}{4})-(x - 2)^{2}]^{2}dx$.

Answer:

B. 3.549