समाकलन अध्धयन -1

 🧮 Integration Practice Questions – Solutions

👉 Q1: ∫3x² dx

Solution:

यहाँ power rule लगाते हैं:

\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

तो,

\int 3x^2 \, dx = 3 \cdot \frac{x^{2+1}}{2+1} + C = 3 \cdot \frac{x^3}{3} + C = x^3 + C

✅ Final Answer:

x^3 + C

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👉 Q2: ∫sin(x) dx

Solution:

\int \sin(x) \, dx = -\cos(x) + C

✅ Final Answer:

-\cos(x) + C

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👉 Q3: ∫1/x dx

Solution:

\int \frac{1}{x} \, dx = \ln|x| + C

✅ Final Answer:

\ln|x| + C

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✅ Summary Chart:

Question Answer

∫3x² dx x³ + C

∫sin(x) dx -cos(x) + C

∫1/x dx ln