# JEE Advanced Mathematics Sample Paper on Application of Integral (Area Under Curve) with Answer & Solution 2019

## Question Paper : Integration Question Paper 01

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## Answer & Solution : Integration Question Paper 01

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In this last chapter of this path we will be taking a seem at a pair of applications of integral.  There are lots of other applications, however many of them require integration techniques that are typically hard in Calculus II.

For the reason that this chapter is inattentive on the applications of integral it is understood in all the examples that you are capable of doing the integral.

1. #### Applications of the Indefinite Integral

Displacement (from velocity) and velocity (from acceleration) using the indefinite integral, how to show. How to find areas of shapes with straight sides, we learn in primary school (e.g. area of a triangle or rectangle).

1. Area Under a Curve and Area Between two Curves
2. Work by a Variable Force

This section includes Hooke’s Law for springs. The work done on an object when the force is not constant, how to discover and show.

1. Volume of Solid of Revolution

Integral to find the volume of an object with curved sides, Explains how to utilize, e.g. wine barrels.

1. Centroid of an Area (Centre of Mass).

Integral to find the centroid of an area with curved sides, We learn how to utilize.

1. Moments of Inertia

The resistance of a rotating body. We use integral when the shape has curved sides, explains how to discover.

1. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the charges. We use integral to calculate the work done when charges are separated.
2. Average Value of a curve can be calculated using integral.
3. We use integral to find the force. Force by Liquid Pressure varies depending on the shape of the object and its depth.

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I can not write in a straight line unless. I have lined papers to help guide me along the pages. However some-times the task calls for plain-paper where no such lines are in place (i.e. a poster or some such).

I usually write with a ball point pen. However, in the case of a poster, I use felt tip pen which is more susceptible to smudging if rubbed too much / too soon!

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I have tried placing a ruler along the page but this messes up my handwriting and it looks a bit weird so I would rather try a new method.

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• Draw thin lines with a pencil and erase them afterwards. If you work with a soft pencil and without much force, the lines are easily erasable and you won`t mark the sheet.
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• Also, you can work at the edge of a table or by placing a ruler under the paper. You will notice directly if you are not on the line. But it will be not beneficial for your style.

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