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**Assignment:**
Evaluate the line integral where \( C \) is the curve given by:
\[
\int_C (e^x + x^2) \, dx + (2xy) \, dy
\]

This is a line integral involving a vector field, and it looks like a problem of evaluating a line integral over a curve \( C \).

To solve this, we need more information about the curve \( C \). The curve could be parameterized, or a particular path might be given.

Would you like to clarify the curve \( C \), or should I assume it is a standard path, such as a straight line or a circle? I can proceed based on these assumptions if needed.

Here are 5 questions to expand on this topic:

1. Do you know the equation or parameterization of the curve \( C \)?
2. Would you like to explore how line integrals are calculated step-by-step?
3. Is this a problem related to a specific type of curve, such as a circle or line segment?
4. Should we approach this problem using Green's Theorem, assuming \( C \) is a closed curve?
5. Are there any conditions or constraints related to the vector field along \( C \)?

**Tip:** In line integrals, knowing how to parameterize the curve is crucial. This reduces the problem to calculating regular integrals over an interval.

Evaluate the line integral where C is the curve: ∫C (e^x + x^2) dx + (2xy) dy

This problem involves evaluating a line integral over a vector field. Learn how to solve the line integral ∫C (e^x + x^2) dx + (2xy) dy, with step-by-step guidance on the role of Green's Theorem and vector fields in multivariable calculus.

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