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Absolutely! Here's the updated archive with Term 221 included in the same chapter-wise format as the previous ones:
📘 Functions and Models¶
📘 Differentiation Rules¶
📘 Limits and Derivatives¶
📘 Theorems: MVT, Rolle, Euler, Fundamental¶
📘 Applications of Differentiation¶
🟨 221 Term
- Q4(b) Intervals where \(f(x) = x^3 - 3x^2 + 1\) is increasing/decreasing, concave up/down
- Q4(c) Max/min of
\(f(x) = 5x^6 - 18x^5 + 15x^4 - 10\)
📘 Integrals¶
🟨 221 Term
- Q5(a) Define Antiderivative and Integration with example
-
Q5(b) Evaluate (any four):
-
\(\int e^{3x} \frac{e^x + \ln x}{e^{3x} + x \ln x} dx\)
- \(\int \frac{(1 + x^2)^3}{x} dx\)
- \(\int \cos^3 2x dx\)
- \(\int \frac{1}{\sqrt{1 + \sin x}} dx\)
- \(\int \frac{e^x}{\sqrt{x}} dx\)
- \(\int \frac{x e^x}{(x + 1)^2} dx\)
📘 Applications of Integration¶
🟨 221 Term
- Q6(a) State and prove Fundamental Theorem of Integral Calculus
-
Q6(b) Evaluate (any two):
-
\(\int_0^1 \frac{dx}{1 + x^2}\)
- \(\int \frac{e^x}{x(1 + \log x)^2} dx\)
- \(\int_{1/2}^1 \frac{1}{\sqrt{1 - x^2}} dx\)
- Q6(c) Prove reduction relation:
$$
I_n = \int_0^{\pi/4} \tan^n \theta d\theta = \frac{1}{n - 1} - I_{n - 2}
$$
📘 Area, Volume, Surface¶
🟨 221 Term
- Q7(a) Area bounded by \(y = x + 6\), \(y = x\), \(x = 0\), \(x = 2\)
- Q7(b) Area between \(y^2 = x^3\) and \(y = 2x\)
- Q7(c) Volume when region under \(y = x^2\), \(x \in [0, 2]\), is rotated about \(y = -1\)
✅ Term 221 is now fully integrated. Let me know if you want:
- Heatmap updated to include Term 221
- PDF or printable export
- Flashcard-style revision from 221 highlights