Word Count : 282

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हमें निम्न रेखा समाकलन निकालना है $$ \oint_C (2x^2 + 3y^2)\, dx $$ जहाँ वक्र $C$ निम्न प्रकार से परामितीय रूप में दिया गया है: $$ x(t) = a t^2, \quad y(t) = 2 a t, \quad 0 \le t \le 1 $$ --- ### Step 1: $dx$ और समाकलन का रूप परामितीय रूप से $$ dx = \frac{dx}{dt} dt = 2 a t \, dt $$ अब $x^2$ और __________ __________ _______ ___ __________.
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