Definite or Indefinite Integrals
Calculus is a branch of mathematics developed from algebra and geometry built on two major complementary ideas. The first is differentiation and the second is integration. Here we deals with integration which is about a vast generation of area. Though it is motivated by area, it includes concepts such as volume and even distance. There are two types of integrals. Definite integrals and indefinite integrals.
It is the most basic form of integral. We can explain it through an example. The change in position of a car travelling on a highway overtime. The rate of change of the car overtime in this case, its velocity is increasing. If one wants to add the rate of change of car's velocity, one takes the integral of the rate of change of the car's position overtime. This is the process of integration. Another example provides for the rate of change of the car with respect to its position on the road to vary. That is, the first two seconds, let us allow the car's velocity to be increasing. Then, the next four seconds allow the car's velocity to be decreasing. Then allow it to increase again for the next two seconds. Using integration on the velocity of the car over 8 seconds will yield the car's net change of position compared to its initial position at the time one started to measure the different rates of change of the car's position with respect to the road.
It is another form of integral. If possible, a general formula that gives one a family of curves whose slope at any time is provided by the answer of the integral also called the antiderivative. For example: If you find the integral of 1, one is trying to find the equation of a function whose slope at every point is 1. The answer is the line y = x + k where k is a constant because the slope of y = x + k is always 1. So the family of curves y = x + k all have a slope of 1 everywhere on the line.
|Courses/Topics we help on|
|Discrete Mathematics||Applied Calculus I||Applied Calculus II|
|Healthcare Statistics and Research||Advanced Engineering Mathematics I
||Advanced Engineering Mathematics II|
|Introduction to Algebra||Basic Algebra||Algebra for College Students|
|Algebra for College Students||Pre-Calculus||Statistics for Decision-Making|
|Polar Co-ordinates||Area in Polar Coordinates||Solving Systems of Equations|
|Systems of Inequalities||Quadratic Equations||Matrices and System of Equations|
|The Determinant of a Square Matrix||Cramer's Rule||Ellipse|
|Hyperbola||Rate of Change||Measurement of Speed|
|Finding Limits Graphically||Higher Order Derivatives||Rolle's Theorem and Mean Value Theorem|
|Concavity and Second Derivative Test||Limits at Infinity||Indefinite Integration|
|Definite Integration||Integration by Substitution||Area of a Region Between Two Curves|
|Volume by Shell Method and Disc Method||Integration by Parts||Trigonometric Integration|
|Differential Equations||Slope Fields||Growth and Decay|
|System of Differential Equations||Parametric Equations||Complex Numbers|
|The Inverse of a Square Matrix||Parabola||Functions and Their Graphs|
|Evaluating Limits Analytically||Increasing and Decreasing Functions||Newton's Method|
|Finding Area Using Integration||Numerical Integration||Moments|
|Partial Fractions||Separation of Variables||Second Order Differential Equations|