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Integrate the following Q. 1.                 Q. 2. Evaluate the following as the limit of a sum.  Q. 3. Evaluate the following:           Q. 4. Find the area the first quadrant enclosed by the x-axis, the line Q. 5. Find the area of the region enclosed by two circles and Q. 6. Using integration find the area of , whose vertices are A(2, 0) B(4, 5) and C(6, 3). Q. 7. Find the area above x-axis and included in circle x2 + y 2 = 8x and the parabola y2 + 4x . Q. 8. Find the area of the region Q. 9. Find the area of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x . Differential equations Q. 1. Form the family of differential equation represented by the curve   Q. 2. Form the differential equation represented circle passing through origin and center lies on x-axis. Q. 3. Solve the differential equations :     Q. 4. Solve the differential equt: x(1 + y2)dx - y(1 + x2)dy = 0. y(1) = 0 (x2+y2) dx + xy dy = 0, y (1)=1 Q. 5. At any point on the curve the slope of tangent is twice the slope of the line joining the point of contact to the point(-4,-3) find the equation of the curve passing through (-2,1). Paper By Mr. Rajput