# Are Length and Sector Area

Home > iitutor You should know with these terms relating to the parts of a circle. The centre of a circle is the point which is equidistant from all points on the circle. A radius of a circle a straight line joining the centre of a circle to any point on the circumference. A minor [...]

Home > iitutor Degree Measurement of Angles One full revolution makes an angle of $360^{\circ}$, and the angle on a straight line is $180^{\circ}$. Therefore, one degree, $1^{\circ}$, can be defined as $\dfrac{1}{360}$ of one full revolution. For greater accuracy we define one minute, $1'$, as $\dfrac{1}{60}$ of one degree and one second, $1''$, as [...]

# Volumes for Two Functions

Home > iitutor If the region bounded by the upper function $y_{upper}=f(x)$ and the lower funciton $y_{lower}=g(x)$, and the lines $x=a$ and $x=b$ is revolved about the $x$-axis, then its volume of revolution is given by: \begin{align} \displaystyle V &= \int_{a}^{b}{\Big([f(x)]^2 - [g(x)]^2\Big)}dx \\ &= \int_{a}^{b}{\Big(y_{upper}^2 - y_{lower}^2\Big)}dx \end{align} Example 1 Find the [...]

# Volumes using Integration

Home > iitutor Volume of Revolution We can use integration to find volumes of revolution between $x=a$ and $x=b$. When the region enclosed by $y=f(x)$, the $x$-axis, and the vertical lines $x=a$ and $x=b$ is revolved through $2 \pi$ or $360^{\circ}$about the $x$-axis to generate a solid, the volume of the solid is given by: [...]

# Kinematics using Integration

Home > iitutor Distances from Velocity Graphs Suppose a car travels at a constant positive velocity $80 \text{ km h}^{-1}$ for $2$ hours. \begin{align} \displaystyle \text{distance travelled} &= \text{speed} \times \text{time} \\ &= 80 \text{ km h}^{-1} \times 2 \text{ h} \\ &= 160 \text{ km} \end{align} We we sketch the graph velocity [...]