https://file.aiquickdraw.com/mathbot/file/1739323435985de3dpjip.jpg

Here are the given math problems from the image:

1. **Find \( f(x) \) given that \( f'(x) = 6x + 1 \) and \( f(2) = 13 \).**
2. **Find the equation of the curve \( y = f(x) \) given that the gradient at any point \((x,y)\) is \( \frac{dy}{dx} = 6x^2 - 2x \) and the curve passes through \( (1,4) \).**
3. **If \( y = 5x - 6 \), determine the equation of the curve passing through \( (2,-1) \).**
4. **Given \( f'(x) = x^2 - 5 \) and \( f(2) = 3 \), find \( f(3) \).**
5. **If \( F'(x) = ax^2 + 2x - 2 \), the second derivative \( F(x) \), and \( F(1) - F(-2) = 0 \), determine the function \( F(x) \).**

Would you like detailed solutions for all problems, or do you want to start with a specific one?  

Here are five related questions to deepen understanding:  
1. How do you find a function from its derivative using integration?  
2. What is the role of initial conditions in solving integration problems?  
3. How do you determine the equation of a curve given a gradient function?  
4. What is the difference between first and second derivatives in a function?  
5. How can definite integrals help solve problems involving function differences?  

**Tip:** When solving for a function from its derivative, always include the constant of integration and use given conditions to find its value.

1. Tentukan fungsi f(x) jika diketahui f'(x) = 6x + 1 dan f(2) = 13
2. Tentukan persamaan kurva y = f(x) jika diketahui gradien garis singgung y = f(x) adalah dy/dx = 6x^2 - 2x dan kurva melalui titik (1,4)
3. Jika y = 5x - 6, tentukan persamaan kurva yang melalui titik (2,-1)
4. Bila f'(x) = x^2 - 5 dan f(2) = 3, tentukan f(3)
5. Jika F'(x) = ax^2 + 2x - 2 turunan dari F(x) dan F(1) - F(-2) = 0, tentukan fungsi F

Learn how to solve derivative and integral problems, including finding functions from derivatives and determining curve equations. This page covers key concepts such as the Fundamental Theorem of Calculus and applying initial conditions for solution. Suitable for students in Grades 10-12.

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