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Area under Curves-Class 12 Maths

Updated: Nov 5

How to evaluate area under Curves?

applications of integrals cover page

Welcome to Areas of Bounded Regions in Class 12 Mathematics. This is in fact an application of Integration and a very useful one. It's taught in High school and in College as part of Multivariable Calculus.

I am Suman Mathews, Maths teacher and content developer. I have taught Math for three decades at the high school and college level and I have helped inspire many young minds to like Mathematics and pursue it further. Using Integration to find the area of bounded regions is an easy topic provided you get it right.

And that's exactly what I'm going to be doing. You could join my online classes for Class 12 Maths. I'll be giving you two simple tricks using which you can solve any question on this topic.

I have taught this topic both at high school and in college. Using this technique, you can calculate area between a curve and a line or area between two curves. First and foremost, you'll need to draw a rough sketch of the curves.

What are the basic curves that you need to know?

You need to keep in mind certain standard curves such as straight lines, lines parallel to the coordinate axes, lines passing through the origin, the modulus function. You'll also need to know basic curve sketching of circles, parabolas and ellipse. So, given the problem,the first step will be to draw a rough sketch.

Once that's done, try to determine the limits, either left and right or bottom and top. Sometimes, if the limits are not clear, you may need to find the points of intersection. This can be done by solving the equations simultaneously.

Question on Applications of Integrals

How to calculate area under curves Class 12 Math?

So, while integrating, either you go from left limit to right limit and integrate from the equation of the top curve- equation of the bottom curve. Or start from bottom limit to top limit and integrate from equation of the right curve - equation of the left curve. Sometimes, you may have to divide the region into two parts and integrate each part separately and then add up the two regions.

So, here's how you calculate area under curves Class 12 Math.

Lesson 1-Finding the area bounded between two curves

Lesson 2-Finding the area bounded between two curves

Lesson on Finding the Area between 2 curves

MCQ-Area of bounded regions

MCQ-Area of the region bounded between 2 parabolas

MCQ-Finding the area of a region bounded between 2 curves

MCQ-Find the area enclosed between 2 curves

Find the area enclosed between a parabola and a line

Do you still need help understanding this chapter?

All these topics and more will be discussed in my online classes. You'll learn how to solve multiple choice questions, assertion based questions, conceptual questions, case study questions and more. What's more, you'll also get access to regular tests which will be graded.

lLet's learn together!

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