- #1
Misswfish
- 6
- 0
If f is continuous on [a,b], f(x) [tex]\geq[/tex] 0 for each x in [a,b] and there is a number p in [a,b] such that f(p) > 0, then [tex]\int[/tex] f dj > 0 ( Note : the integral is from a to b)
Misswfish said:but how does the def of continuous show that the integral is greater than zero
Analysis 2 is a branch of mathematics that focuses on understanding and solving problems related to integrals, which are mathematical expressions used to calculate areas and volumes. It is an important tool for various fields of science, such as physics, engineering, and economics.
Some common techniques used in Analysis 2 for solving integrals include substitution, integration by parts, partial fractions, and trigonometric substitution. These methods allow for the simplification and manipulation of integrals to make them easier to solve.
Definite integrals have specific values for the upper and lower limits of integration, while indefinite integrals do not have any limits. Definite integrals are used to find the exact value of an integral, while indefinite integrals are used to find the general solution of an integral.
One way to check if your integral solution is correct is to take the derivative of your solution and see if it matches the original function. Additionally, you can use online integral calculators or plug your solution into a graphing calculator to visually see if it matches the original function.
Analysis 2 and integrals have many real-life applications, including calculating areas and volumes in engineering and physics, determining the average value of a function in economics, and analyzing population growth in biology. They are also used in various other fields, such as computer science, statistics, and finance.