R K M.

Piyush Raj 6 hrs ago There are 8 methods of integration:- 1) The general formula 2) The basic logarithmic forms. 3) The exponential form 4) The basic trigonometric forms 5) Other trigonometric forms 6) Inverse trigonometric forms 7) Integration by parts (ILATE) 8) Integration by partial fraction

Graduate Aptitude Test in Engineering (GATE) is an all-India examination administered and conducted jointly by the Indian Institute of Science and seven Indian Institutes of Technology on behalf of the National Coordinating Board - GATE, Department of Education, Ministry of Human Resource Development (MHRD), Government of India.The GATE Exam committee, which comprises of representatives from the administering institutes, is the sole authority for regulating the examination and declaring the results. GATE is conducted through the constitution of eight zones. The zones and the corresponding administrative institutes are:

Property 1: Tangents drawn from a common point, outside the curve are equally inclined to the focal points. PROPERTY 2 A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p. PROPERTY 3 The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis. PROPERTY 4 Conjugate Diameters Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s. Constructing the Ellipse given the Conjugate Diameter PROCEDURE 1. Construct the conjugate diameters TU (long) and RS (short). 2. Take a line from R perpendicular to TU of length CU to find point D. 3. Join D to C. 4. Construct a circle of diameter DC. 5. Take a line from R through the centre of the circle and project it on to meet the circle at G. 6. A line from G through C will give the direction of the minor axis. 7. RE = 1/2 the minor axis. 8. A line from E through C will give the direction of the major axis. 9. RG = 1/2 the major axis. 10. You now have the major and minor axis and can construct the curve. NOTE: The curve passes through points R, S, T and U. PROPERTY 1 Tangents drawn from a common point, outside the curve are equally inclined to the focal points. PROPERTY 2 A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p. PROPERTY 3 The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis. PROPERTY 4 Conjugate Diameters Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s. Constructing the Ellipse given the Conjugate Diameter PROCEDURE 1. Construct the conjugate diameters TU (long) and RS (short). 2. Take a line from R perpendicular to TU of length CU to find point D. 3. Join D to C. 4. Construct a circle of diameter DC. 5. Take a line from R through the centre of the circle and project it on to meet the circle at G. 6. A line from G through C will give the direction of the minor axis. 7. RE = 1/2 the minor axis. 8. A line from E through C will give the direction of the major axis. 9. RG = 1/2 the major axis. 10. You now have the major and minor axis and can construct the curve. NOTE: The curve passes through points R, S, T and U.