8. Define Beta function. Apply Beta and Gamma function to evaluate (x 2ax-xdx 9. Find the...

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8. Define Beta function. Apply Beta and Gamma function to evaluate (x 2ax-xdx 9. Find the area common to the circle r = a and the cordioid r = a(1+cose) 10. Through what angle should the axes be rotated to reduce the equation 3x+2xy + 3y-2x=0 into one with the xy term missing? Also obtain the transformed equation. 11. Derive the equation of an ellipse in standard form. 12. Find the product of semi-axis of the conic x-4xy+5y = 2 OR 12 Describe and sketch the graph of conic r=- 3+2 cos 13. Solve the differentiate equation of (x-y)dx+2xydy=0 14. Solve: y = yp+2px where p =- dy dx 15. Solve (D2-6D+9)y = xe* 8. Define Beta function. Apply Beta and Gamma function to evaluate (x 2ax-xdx 9. Find the area common to the circle r = a and the cordioid r = a(1+cose) 10. Through what angle should the axes be rotated to reduce the equation 3x+2xy + 3y-2x=0 into one with the xy term missing? Also obtain the transformed equation. 11. Derive the equation of an ellipse in standard form. 12. Find the product of semi-axis of the conic x-4xy+5y = 2 OR 12 Describe and sketch the graph of conic r=- 3+2 cos 13. Solve the differentiate equation of (x-y)dx+2xydy=0 14. Solve: y = yp+2px where p =- dy dx 15. Solve (D2-6D+9)y = xe*