MAHE Manipal B.Sc Nursing 2025
ApplyAccorded Institution of Eminence by MoE, Govt. of India | NAAC A++ Grade | Ranked #4 India by NIRF 2024
44 Questions around this concept.
The motion of a particle along a straight line is described by the equation: x = 8 + 12 t - t3 where x is in metres and t in seconds. The retardation of the particle when its velocity becomes zero, is:
Differentiation
Differentiation is very useful when we have to find rates of change of one quantity compared to another.
If y is one quantity and we have to find the rate of change of y with respect to x which is another quantity
Then the differentiation of y w.r.t x is given as
For a y V/s x graph
We can find the slope of graph using differentiation
I.e Slope of y V/s x graph =
Some important Formulas of differentiation
Example-
Similarly
Integration
Opposite process of differentiation is known as integration.
Let x, y are two quantities
Using differentiation we can find the rate of change of y with respect to x
Which is given by
But using integration we can get direct relationship between quantities x and y
So let where K is constant
Or we can write
Now integrating on both sides we get direct relationship between x and y
I.e
Where C is some constant
For a y V/s x graph
We can find the area of graph using integration
Some important Formulas of integration
where (C = constant)
E.g-
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