Introduction to Analytical Geometry & Integration
Unit 4 bridges geometry and calculus. ‘Analytical Geometry’ teaches you how to plot data points and find trends (Slope) on a graph—essential for analyzing lab results. ‘Integration’ is the tool used to calculate area under the curve (AUC), which represents total drug exposure in the body.
Syllabus & Topics
- 1Analytical Geometry: Signs of Coordinates, Distance formula
- 2Straight Line: Slope (m), Conditions for parallel/perpendicular lines
- 3Slope of line joining two points, Slope–intercept form (y = mx + c)
- 4Integration: Definition, Standard formulae
- 5Rules of integration (Sum, Difference, Constant multiple)
- 6Integration Methods: Substitution, Partial fractions, Integration by parts
- 7Definite Integrals: Concept and Application (Area under curve)
Learning Objectives
Frequently Asked Questions (FAQs)
Q1. What is Analytical Geometry?
Analytical Geometry (Coordinate Geometry) is the study of geometric figures using a coordinate system (x–y plane). It helps describe positions, distances, and shapes using algebraic equations.
Q2. What is the Distance Formula?
The distance between two points (x1,y1) and (x2,y2) is given by:
Q3. Slope-Intercept Form of a Line?
The equation of a straight line in slope–intercept form is:
y = mx + c
where m is the slope (gradient) and c is the y-intercept.
Q4. What is Integration?
Integration is the reverse process of differentiation. It is used to find the area under a curve, volume, or the total accumulation of a quantity, such as total drug absorbed over time.
Q5. Difference between Definite and Indefinite Integral?
Indefinite Integral: Has no limits and includes a constant (+C)
Definite Integral: Has fixed limits [a, b] and gives a specific numerical value (area under the curve)