Class 12 Math: Integrals Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 12 Integrals to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (HARD)

Using integration, find the area of region bounded by line y = 3x , the curve y = 24 x- and y- axis in first quadrant.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Given equations are y = 3x and y = 24 x- Squaring both side, we get x² + y² = 4 Intersection point of x² + y² = 4 and y = 3x x² + 3x² = 4 ⇒ x = ± 1 Intersection point in I Quadrant is (1, √3)

Question 2 (EASY)

The integrated factor of the differential equation: (1+x2) dy dx+y=e tan-1x is
  • Option 1: 1 ௘೟ೌ೙-1ೣ
  • Option 2: 2 etan-1x
  • Option 3: 3etan-1x
  • Option 4: etan-1x

Solution Explanation & Steps: (d) etan-1x

Question 3 (HARD)

Make a rough sketch of the region {(x,y ):0 ≤y≤x2+ 1,0 ≤y≤x+1,0 ≤x≤ 2} and find the area of the region using integration.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Required Area=∫ (x2+ 1) 1 ଴xd+∫ (x+1) 2 1xd = 23 ଺

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 12 Math Resource Hub for Integrals: • 🧮 Interactive Solver: Solve Integrals Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Integrals Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Integrals PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Integrals Key Equations - Complete revision references. • 🔄 Next Topic Guide: Application of Integrals Study Notes • 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.