Why do we need to study Integration?
by M. Bourne
Often we know the relationship involving the rate of change of two variables, but we may need to know the direct relationship between the two variables. For example, we may know the velocity of an object at a particular time, but we may want to know the position of the object at that time.
To find this direct relationship, we need to use the process which is opposite to differentiation. This is called integration (or antidifferentiation).The processes of integration are used in many applications.
The Petronas Towers in Kuala Lumpur experience high forces due to winds. Integration was used to design the building for strength
Historically, one of the first uses of integration was in finding the volumes ofwine-casks(which have a curved surface).
The Sydney Opera House is a very unusual design based on slices out of a
ball. Many differential equations (one type of integration)
were solved in the design of this building.
Trigonometry in Astronomy
Model of Solar System
Trigonometric tables were created over two thousand years ago for computations in astronomy. The stars were thought to be fixed on a crystal sphere of great size, and that model was perfect for practical purposes. Only the planets moved on the sphere. (At the time there were seven recognized planets: Mercury, Venus, Mars, Jupiter, Saturn, the moon, and the sun. Those are the planets that we name our days of the week after. The earth wasn't yet considered to be a planet since it was the center of the universe, and the outer planets weren't discovered then.) The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry. Spherical trigonometry is rarely taught now since its job has been taken over by linear algebra. Nonetheless, one application of trigonometry is astronomy.
INVERSE TRICONOMETRIC FUNCTIONS
The glideslope subsystem radiates a signal from the ground providing elevation