Class 12 Math: 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 Integrals.
Step-by-Step Solved Problems
Example 1: Integration by Substitution
Question: Evaluate: ∫ 2x cos(x²) dx.
Worked Solution Steps:
- Let u = x² => du = 2x dx.
- Substitute in integral: ∫ cos(u) du.
- Integrate: sin(u) + C.
- Replace u: sin(x²) + C.
Final Answer: \sin(x^2) + C
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 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.