Find the value of the line integral [10xy dx+ +12) dy, where C is an ellipse (3,0) to (0,2). C (Hint: If F(x,y) = 10xyi+ (5x² + y²)j + = 1 from 4 is conservative, the integration may be easier on an alternate path.)

Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.

Calculate the line integral f (−xy³ − 6x + 6y − 3) dx + (−5xy − 3) dy, - where C' is the rectangle with vertices (-2, 1), (2, 3), (-4, 3), and (-4,1) oriented clockwise. Enter an exact answer. Provide your answer below: f(-x³-6x+6y-3) dx + (−5xy − 3)dy =

Find the integration factor of (3xy + 6y²) dx + (2x²gxy) dy =o