Integration | अभिन्न

Important Concepts | महत्वपूर्ण अवधारणाएँ

• Integration is the reverse process of differentiation. | अभिन्नीकरण अवकलन की विपरीत प्रक्रिया है।
• Basic Formulas: ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C (for n ≠ -1) | मूल सूत्र: ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C (n ≠ -1 के लिए)
• ∫e^x dx = e^x + C | ∫e^x dx = e^x + C
• ∫1/x dx = ln|x| + C | ∫1/x dx = ln|x| + C

Step-by-Step Hint Questions | चरणबद्ध संकेत प्रश्न

1. ∫x² dx = ?
   
   Step-by-Step Hint | चरणबद्ध संकेत

   Step 1: Identify n = 2
   Step 2: Use formula ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C
   Step 3: Apply: (x³)/3 + C
   Final Answer: (x³)/3 + C
2. ∫1/x dx = ?
   
   Step-by-Step Hint | चरणबद्ध संकेत

   Step 1: This is a standard integral.
   Step 2: Apply formula: ∫1/x dx = ln|x| + C
   Final Answer: ln|x| + C
3. ∫e^x dx = ?
   
   Step-by-Step Hint | चरणबद्ध संकेत

   Step 1: Recognize the exponential function.
   Step 2: Apply ∫e^x dx = e^x + C
   Final Answer: e^x + C
4. ∫cos(x) dx = ?
   
   Step-by-Step Hint | चरणबद्ध संकेत

   Step 1: Apply trigonometric integration rule.
   Step 2: ∫cos(x) dx = sin(x) + C
   Final Answer: sin(x) + C
5. ∫1/(1+x²) dx = ?
   
   Step-by-Step Hint | चरणबद्ध संकेत

   Step 1: Recognize inverse trigonometric form.
   Step 2: Apply ∫1/(1+x²) dx = tan⁻¹(x) + C
   Final Answer: tan⁻¹(x) + C

Practice Questions | अभ्यास प्रश्न

• ∫x dx = ?
• ∫sec²(x) dx = ?
• ∫ln(x) dx = ?
• ∫x³ dx = ?
• ∫1/√x dx = ?