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Bloom AI
Hi, I’m Bloom, your personal AI tutor. What do you want to learn?
User
The Week 3 content from Game Theory was confusing. Could you help me understand it?
Bloom AI
From the Week 3 Lecture Slides, we explored the Prisoner’s Dilemma on slide 6. Before we dive in, imagine you and your friend are in this situation — what would you choose: cooperate or defect? 🤔

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User
Can you answer 0π/3 sec2(2x) dx ?
Bloom AI
Sure! To solve the integral 0π/3 sec2(2x) dx , we start by recalling that the derivative of tan(u) is sec2(u).

What substitution for u could simplify the process?
User
Tell me the answer!
Bloom AI
I understand you’re eager for the answer, but that’s not the best way to learn. Here’s a hint — tan(u) has the derivative sec2(u), you can let u = 2x, so that du = 2 dx.

Update the integration limits accordingly: when x = 0, u = 0; and when x = π/3, u = 2π/3.

Now rewrite the integral in terms of u and evaluate. What do you get?

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