Integrals
Madhya Pradesh Board · Class 12 · Mathematics
Flashcards for Integrals — Madhya Pradesh Board Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allहल करें: ∫ x^3 dx
Answer
समाकलन के लिए घात नियम का प्रयोग करें। चरण 1: घात को 1 से बढ़ाएँ → x^(3+1) = x^4। चरण 2: नए घात से भाग दें → x^4/4। चरण 3: समाकलन के स्थिरांक को जोड़ें। उत्तर: ∫ x^3 dx = x^4/4 + C…
Solve: ∫ x^3 dx
Answer
Use the power rule for integration. Step 1: Increase the power by 1 → x^(3+1) = x^4. Step 2: Divide by the new power → x^4/4. Step 3: Add the constant of integration. Answer: ∫ x^3 dx = x^4/4 + C…
Solve: ∫ (3x^2 + 4x^3) dx
Answer
Use the sum rule and integrate term by term. Step 1: ∫ 3x^2 dx = 3 · x^3/3 = x^3. Step 2: ∫ 4x^3 dx = 4 · x^4/4 = x^4. Step 3: Combine the results. Answer: x^3 + x^4 + C…
हल करें: ∫ (3x^2 + 4x^3) dx
Answer
योग नियम का उपयोग करें और पद दर पद समाकलन करें। चरण 1: ∫ 3x^2 dx = 3 · x^3/3 = x^3. चरण 2: ∫ 4x^3 dx = 4 · x^4/4 = x^4. चरण 3: परिणामों को मिलाएं। उत्तर: x^3 + x^4 + C…
हल कीजिए: ∫ (sin x + cos x) dx
Answer
प्रत्येक पद को अलग-अलग इंटीग्रेट करें। चरण 1: ∫ sin x dx = -cos x. चरण 2: ∫ cos x dx = sin x. चरण 3: परिणामों को जोड़ें और C को शामिल करें। उत्तर: -cos x + sin x + C…
Solve: ∫ (sin x + cos x) dx
Answer
Integrate each term separately. Step 1: ∫ sin x dx = -cos x. Step 2: ∫ cos x dx = sin x. Step 3: Add the results and include C. Answer: -cos x + sin x + C…
Solve: ∫ (1/x) dx
Answer
This is the special case of the power rule that must be handled separately. Step 1: Recognize that n = -1 is excluded from the power rule. Step 2: Use the logarithmic form. Answer: ∫ (1/x) dx = log |x…
समाधान कीजिए: ∫ (1/x) dx
Answer
यह घात नियम का विशेष मामला है जिसे अलग से हल करना होगा। चरण 1: पहचानें कि n = -1 is excluded from the power rule. चरण 2: लघुगणकीय रूप का उपयोग करें। उत्तर: ∫ (1/x) dx = log |x| + C…
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