10.3 - Step-by-Step Procedure
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Practice Questions
Test your understanding with targeted questions
Integrate \( \frac{\partial z}{\partial x} = 5x \).
💡 Hint: Remember to treat y as a constant.
What is the result of integrating \( \frac{\partial z}{\partial y} = 3y^2 \)?
💡 Hint: Think about what happens to x during this integration.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is direct integration used for?
💡 Hint: Think about which type of equations involve partial derivatives.
When given \( \frac{\partial z}{\partial x} = f(x,y) \), we integrate with respect to which variable?
💡 Hint: This ensures we correctly find \\( z \\) as a function of both variables.
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Challenge Problems
Push your limits with advanced challenges
Given the PDEs \( \frac{\partial z}{\partial x} = 3x^2 \) and \( \frac{\partial z}{\partial y} = 4y \), derive the function z.
💡 Hint: Remember to add both arbitrary functions after integration.
For the PDE \( \frac{\partial z}{\partial x} = sin(xy) \), integrate to find z where y is treated as constant.
💡 Hint: Recall how we adjust our integration based on treating y as a constant.
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