Mathematical Tools - Practice Questions & MCQ

1. 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

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Example-

Similarly 

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2. 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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