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Solution to Excerses of The Fundamental Theorem of Calculus and Indefinte Integrals

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Calculus Lectures - Integral Summary

Basic integrals to be memorized clearly - integrals of power, exponential, logarithm and basic trigonometric functions Other important integrals of trigonometric functions Other important integrals of trigonometric functions - Continue An important integration technique - Trigonometric substitutions Integrals of Inverse Trigonometric functions

Calculus Lectures - Derivative Summary

Concept of differentiability, derivative and derivative function Differentiation Rules Derivatives of Power, Exponential and Logarithmic Functions Derivatives Trigonometric and Inverse Trigonometric Functions Obtain the derivative of inverse trigonometric functions with implicit differentiation 1. Obtain the derivative of inverse sine function with implicit differentiation 2. Obtain the derivative of inverse cosine function with implicit differentiation Obtain the derivative of inverse cosine function from the derivative of inverse sine function 3. Obtain the derivative of inverse tangent function with implicit differentiation 4. Obtain the derivative of inverse cotangent function with implicit differentiation 5. Obtain the derivative of inverse secant function with implicit differentiation 6. Obtain the derivative of inverse cosecant function with implicit differentiation Obtain the derivative of inverse cosecant function from the de...

Vector Concepts

Vector definition,addition subtraction and scalar multiplication Key examples for solid understanding of Vector definition,addition subtraction and scalar multiplication The scalar product(dot product, inner product) of 2 vectors Vector projection and example Cross product of 2 vectors Lines and planes 4 key aspects about lines and planes: 1.Equations: vector form, parametric form and Cartesian form, conversion between different forms, find the equations(ie,give 2 points to find the equation of a line, give 3 points to find the equation of a plane, give 2 lines to find the equation of a plane, give a equation of a plane to find another plane which is parallel to the given plane). 2.Intersections: line and line, line and plane, plane and plane. Line and line could have no intersection because they are parallel or skew. To find the intersection between a line and plane, just plug the parametric format of the line to the...