Integral+Calculus

Chapter Four __Inte__g__ral Calculus__  ﻿ Section One: Antiderivatives Section Two: Indefinite Integrals Section Three: Definite Integrals and the Fundamental Theorem of Calculus Section Four: Integration Techniques Section Five: Properties of Definite Integrals Section Six: Riemann Sums Section Seven: Estimation Area Using Rectangles and Trapezoids Section Eight: Area Section Nine: Volumes of Solids of Revolution Section Ten: Volume with Known Cross Sections Section Eleven: Average Value / Mean Value Theorem for Integrals Section Twelve: Differential Equations Section Thirteen: Slope Fields Section Fourteen: Integration on the Calculator   Return to: Differentiation on the Calculator We know that Differential Calculus is the study of change at a given instant, and how to differentiate a function to find formulas that yield that function's rate of change.

Now we are ready to begin the study of the accumulation of a variable's changes to produce a function. In other words, we will be studying the area under curves, or the study of Integral Calculus.

**﻿Example 1**
//Willie pours a concentrated Hydrochloric Acid (HCl) into a beaker at a rate of 100mL per minute.// //If he pours continuously for three minutes, how much HCl has he poured?//

As a simple unit conversion, the amount of HCl poured = 3 minutes x 100mL/minute = 300mL. However, look at a graph of the rate function over time: Did you notice that the amount poured, 300mL, happens to be the same as the area under the rate function from time 0 min to time 3 min? In fact, the quantity function will always eqaul the area under the rate function for a given time as it is still Quantity = rate x time.