Application of Integrals: Class 12 Mathematics (UP Board) important questions and practice
Application of Integrals is chapter 8 of 13 in UP Board Class 12 Mathematics. Below are the topics the paper draws from, the question types that come up again and again, and a free practice test on this chapter alone.
Topics in this chapter
- Area under simple curves using definite integrals
- Area bounded by a curve and a line
- Area of a circle, ellipse and parabola by integration
- Area between the x-axis or y-axis and a curve with correct limits
- Sketching the region before integrating
What examiners usually ask
- Find the area of the region bounded by the ellipse x^2/16 + y^2/9 = 1
- Using integration, find the area of the region bounded by the parabola y^2 = 4x and the line x = 3
- Find the area enclosed between the circle x^2 + y^2 = 4 and the lines x = 0 and x = 2 in the first quadrant
Exam tip
Draw a rough sketch and shade the region first, then use symmetry (multiply by 2 or 4) to simplify limits; area between two curves is removed from the rationalised CBSE syllabus, so focus on curve-and-line regions and standard curves.
Application of Integrals on other boards and exams
Frequently asked questions
What are the important questions from Application of Integrals for UP Board Class 12?
The question types listed above repeat most often in UP Board Class 12 Mathematics papers for this chapter. Practise them with the chapter test and then attempt them inside a full previous-year paper under time.
Is Application of Integrals in the UP Board Class 12 Mathematics syllabus?
Yes. Application of Integrals is part of the current UP Board Class 12 Mathematics syllabus, as listed on this site from the prescribed textbook.
Can I practise Application of Integrals MCQs in Hindi?
Yes. The chapter test and explanations are available in Hindi and English, with an AI doubt solver for any question.