IB Mathematics Applications & Interpretation Topic…

Let $y=\cos^6(3x)$ .

Consider the function $h(x)=4-3\sin(3x)\cos^5(3x)$ , defined for $0\le x\le \frac{\pi}{6}$ .

The region $R$ is bounded by the graph of $h$ , the $x$ -axis, the $y$ -axis, and the line $x=\frac{\pi}{6}$ .

the derivative $\frac{dy}{dx}$ .

Using your result from the previous part, find .

Consider the finite region $R$ bounded by the curve $y = \ln(2x+1)-1$ , the -axis and the -axis.

The side profile of a vase is modelled by the curve $y=g(x)=5-\sqrt{2x+1}$ for .

Let $y=\sin^5(2x)$ .

Consider the function $g (x) = 3 -$ , defined for .

Lengths in this problem are measured in centimetres. Consider the function $r(x)=1+\sqrt{x}$ , defined for . A candle is formed by rotating the region between the curve and the -axis through about the -axis.

a definite integral that represents the area of $R$ .

the precise area of $R$ .

a definite integral to the area of $R$ .

the total area of $R$ .

the $x$ -coordinate of the point where the graph of $g$ intersects the $x$ -axis.

The area bounded by the curve $g$ , the $y$ -axis, and the $x$ -axis is revolved $360^\circ$ around the $x$ -axis. the volume of the resulting solid of revolution.

the derivative $\frac{dy}{dx}$ .

Using your result from the previous part, find $\int \sin^4(2x)\cos(2x)\,dx$ .

a definite integral that represents the area of $S$ .

the precise area of $S$ .

the total volume of the candle.

As the candle burns, the volume $W$ cm $^3$ of wax remaining after $t$ hours is modeled by $W=\frac{68\pi}{3}e^{-0.25t}$ . the time elapsed until half the candle remains.

IB Mathematics Applications & Interpretation AHL 5.12—areas Under a Curve Onto x or y Axis. Volumes of Revolution About x and y Questionbank

IB Mathematics Applications & Interpretation AHL 5.12—areas Under a Curve Onto x or y Axis. Volumes of Revolution About x and y Questionbank

IB Mathematics Applications & Interpretation AHL 5.12—areas Under a Curve Onto x or y Axis. Volumes of Revolution About x and y Questionbank

IB Mathematics Applications & Interpretation AHL 5.12—areas Under a Curve Onto x or y Axis. Volumes of Revolution About x and y Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 5.12—areas Under a Curve Onto x or y Axis. Volumes of Revolution About x and y Questionbank