Most frequently asked questions in Application of Integrals in class 12 mathematics are from the following concepts.
- Area under a Curve – Finding the area enclosed between curves and the x-axis or y-axis.
- Example: Using definite integration to compute the area of a given bounded region.
- Application in Determining the Shaded Area in Conics – Problems based on finding the area of regions defined by conic sections such as circles, parabolas, and ellipses.
- Definite Integral as a Limit of Sum – Understanding the fundamental theorem of calculus and applying it to sum-based integration problems.
- Integral Problems Using Partial Fractions – Solving integration problems by breaking rational functions into simpler fractions before integration.
- Integral by Parts – Applications involving Bernoulli’s formula for solving integration problems.
- Word Problems Using Integration – Real-life applications such as:
- Finding the volume of solids of revolution
- Determining work done in physics using integration
- Calculating population growth models
- Finding the Volume of Solids Using Integration – Applying integral calculus to compute the volume of irregular solids and revolved shapes.
- Indefinite Integrals and Antiderivatives – Understanding basic integration techniques and their applications.
These topics are critical for scoring well in board exams and are also useful for competitive exams like JEE and CUET besides the board examinations viz., CBSE and TN STATE Board.
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