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# Relation Mapping (IIT JAM 2014) ## Question 33 - Relation-Mapping (IIT JAM 2014)

A beautiful problem involving the concept of relation-mapping from IIT JAM 2014.

Let be a differentiable function such that for all and . Then equals

• • • • ### Key Concepts

Relation/Mapping

Differentiation

Integration

Answer: .

Question 33 (IIT JAM 2014)

Real Analysis (Willy)

## Try with Hints

The above problem can be done in many ways we will try to solve this by the simplest method.

Now, as the function is given as So first try to change this into . Try this. It's very easy !!!

To change into we can easily do Now we have to find the value of so we have to change the second degree term, i.e., into some linear form. Can you cook this up ???

Let us assume i.e., Now you know from previous knowledge that integration is also known as anti-derivative. So can be changed into by integrating it with respect to . Try to do this integration and we are half way done !!!

On integrating both side w.r.t we get : , (where is a integrating constant.)

Now we find the value to We know  i.e., Can you find the answer now ?

Now simply, putting we get ## Question 33 - Relation-Mapping (IIT JAM 2014)

A beautiful problem involving the concept of relation-mapping from IIT JAM 2014.

Let be a differentiable function such that for all and . Then equals

• • • • ### Key Concepts

Relation/Mapping

Differentiation

Integration

Answer: .

Question 33 (IIT JAM 2014)

Real Analysis (Willy)

## Try with Hints

The above problem can be done in many ways we will try to solve this by the simplest method.

Now, as the function is given as So first try to change this into . Try this. It's very easy !!!

To change into we can easily do Now we have to find the value of so we have to change the second degree term, i.e., into some linear form. Can you cook this up ???

Let us assume i.e., Now you know from previous knowledge that integration is also known as anti-derivative. So can be changed into by integrating it with respect to . Try to do this integration and we are half way done !!!

On integrating both side w.r.t we get : , (where is a integrating constant.)

Now we find the value to We know  i.e., Can you find the answer now ?

Now simply, putting we get ## Subscribe to Cheenta at Youtube

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