Class 12 Math: Application of Integrals Solved Examples & Step Solutions
NexPro Tools Mathematics TeamJune 5, 20266 min read
The best way to gain confidence in mathematics is by studying solved examples. By analyzing how formulas are applied step-by-step, you learn how to tackle complex questions in your homework and exams. Let's walk through standard worked examples for Class 12 Application of Integrals.
Step-by-Step Solved Problems
Example 1: Area Bounded by Parabola
Question: Find the area bounded by the curve y = x², the X-axis, and lines x = 1 and x = 3.
Worked Solution Steps:
- Set up integral: ∫₁³ x² dx.
- Evaluate antiderivative: [x³ / 3]₁³.
- Calculation: (3³ / 3) - (1³ / 3) = 27/3 - 1/3 = 26/3.
Final Answer: 26/3
Self-Practice Method
When studying these examples, cover the solution with a sheet of paper and attempt to solve the question on your own. If you get stuck, reveal the steps one by one to identify where your logic deviated. This active recall method builds long-term problem-solving skills.
📚 Class 12 Math Resource Hub for Application of Integrals:
• 🧮 Interactive Solver: Solve Application of Integrals Problems - Verify steps in real-time.
• 📝 Timed Practice Quiz: Take Application of Integrals Online Quiz - Test your speed and concepts.
• 📄 Printable Worksheet: Download Application of Integrals PDF Worksheet - Interactive problems with answers.
• 📐 Formula Sheet: View Application of Integrals Key Equations - Complete revision references.
• 🔄 Next Topic Guide: Differential Equations Study Notes
• 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.