Formulas for integration and derivatives

In summary, the speaker is asking for help finding formulas for integration and derivatives, specifically for e^x. They have tried Google but the results were not comprehensive enough. Another person suggests a helpful link.
  • #1
Lunaxia
2
0
Hey guys,

I was wondering if anyone can post up the formulas for integration and derivatives for everything, or if you have a link you can send me to see them. Like taking the integral or derivative of e^x I'd like to know the process for how it works.
 
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  • #2
Lunaxia said:
Hey guys,

I was wondering if anyone can post up the formulas for integration and derivatives for everything, or if you have a link you can send me to see them. Like taking the integral or derivative of e^x I'd like to know the process for how it works.

Have you tried Google?
 
  • #4
phinds said:
Have you tried Google?

I have tried Google but the ones I got were helpful but didn't have everything I needed to know, no steps and didn't show some integrals or derivatives.
 

What is the difference between integration and differentiation?

Integration and differentiation are two fundamental concepts in calculus. Integration is the process of finding the area under a curve, while differentiation is the process of finding the rate of change of a function at a specific point. In other words, integration involves finding the whole from its parts, while differentiation involves finding the parts from the whole.

What are the basic rules for integration and differentiation?

There are several basic rules for integration and differentiation, including the power rule, product rule, quotient rule, and chain rule. The power rule states that the derivative of x^n is n*x^(n-1), while the integration of x^n is (x^(n+1))/(n+1) + C. The product rule states that the derivative of f(x)*g(x) is f(x)*g'(x) + f'(x)*g(x), while the integration of f(x)*g(x) is ∫f(x)*g(x)dx = f(x)∫g(x)dx + ∫f'(x)∫g(x)dx. The quotient rule states that the derivative of f(x)/g(x) is (f'(x)*g(x) - f(x)*g'(x))/(g(x))^2, while the integration of f(x)/g(x) is ∫f(x)/g(x)dx = ∫f(x)∫g(x)dx - ∫f'(x)∫g(x)dx. The chain rule states that the derivative of f(g(x)) is f'(g(x))*g'(x), while the integration of f(g(x)) is ∫f(g(x))*g'(x)dx.

What are the common types of integration problems?

There are several common types of integration problems, including basic integrals, trigonometric integrals, substitution integrals, integration by parts, and partial fraction decomposition. Basic integrals involve using the integration rules to find the antiderivative of a function. Trigonometric integrals involve using trigonometric identities and substitution to solve integrals involving trigonometric functions. Substitution integrals involve substituting a variable in the integral to simplify it. Integration by parts involves using the product rule in reverse to find the integral of a product of two functions. Partial fraction decomposition involves breaking down a rational function into simpler fractions and integrating each term separately.

What are the main applications of integration and differentiation?

Integration and differentiation have numerous applications in various fields, including physics, engineering, economics, and statistics. In physics, integration is used to find the position, velocity, and acceleration of an object, while differentiation is used to find the force and momentum of an object. In engineering, integration and differentiation are used to solve problems related to motion, heat transfer, and signal processing. In economics, they are used to analyze supply and demand curves and optimize production and profit. In statistics, integration and differentiation are used to find the probability density function and cumulative distribution function of a random variable.

How can I improve my skills in solving integration and differentiation problems?

The best way to improve your skills in solving integration and differentiation problems is to practice regularly. Start by understanding the basic rules and techniques, then work on various types of problems, gradually increasing the difficulty level. You can also seek help from textbooks, online resources, or a tutor to clarify any doubts and learn new strategies. Additionally, try to apply these concepts to real-world scenarios to better understand their applications. With consistent practice and determination, you can improve your skills and become proficient in solving integration and differentiation problems.

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