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The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
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What is the value of the rate constant?
I depends on the problem. The rate constant is different depending on the problem in which it occurs.
Is there a constant in the problem of 46n?
the coefficient is 46 and the constant is 0
How do you find the derivative for f(x) integral (1-t2)(1 plus t4) from sin2x to 1?
My suggestion is to multiply the binomials and do the integration directly, and then differentiate the result with respect to x. (If that doesn't work, feel free to send me a picture of the problem and I'll give it another try.)
What is the difference between vertical and horizontal integration?
Horizontal integration is the process of merging similar industries, industries that produce similar products. Vertical integration is the process of buying out suppliers of that particular industry. The main difference is that horizontal integration buys the competing companies while vertical integration aims at the raw material sources necessary to produce that product
What is the indefinite integral of 2x ln2x dx?
In order to work out this problem, we need to learn how to apply the integration method correctly.The given expression is ∫ 2xln(2x) dx.Instead of working out with 2x's, we let u = 2x. Then, du = 2 dx or du/2 = dx. This method is both valid and easy to avoid working out with too much expressions. You should get:∫ uln(u) (du/2)= ½ ∫ uln(u) duUse integration by parts, which states that:∫ f(dg) = fg - ∫ g(df)We let:f = ln(u). Then, df = 1/u dudg = u du. Then, g = ∫ u du = ½u²Using these substitutions, we now have:½(½u²ln(u) - ½∫ u du)= ¼(u²ln(u) - ∫ u du)Finally, by integration, we obtain:¼ * (u²ln(u) - ½u²) + c= 1/8 * (2u²ln(u) - u²) + c= 1/8 * (2(2x)²ln(u) - (2x)²) + c= 1/8 * (2x)² * (2ln(u) - 1) + c= ½ * x² * (2ln(2x - 1)) + c
Why is it important to introduce constant of integration immediately when the integration is performed?
I'm assuming you are asking why you cannot work through your simplification and only put a constant on the last line. The simplest answer is that mathematicians are picky people, and when working through a problem EVERY line must make absolute mathematical sense. Leaving the constant off until the last line makes every line between the point where the integration occurs and the last line false. (Unless you are lucky and the constant of integration is 0, however this still needs to be proven)
Why a constant is written after integrating?
Integration is the opposite of differentiation (taking the derivative). The derivative of a constant is zero. Integration is also called antidifferentiation since integration and differentiation are opposites of each other. The derivative of x^2 is 2x. The antiderivative (integral) of 2x is x^2. However, the derivative of x^2 + 7 is also 2x. Therefore, the antiderivative of 2x is x^2 + C, in general, where the constant C has to be determined from the context of the problem. In the above case, the constant happens to be C=7. We use integration to solve first order differential equations. When solving first order differential equations, like in "word problems", you must determine the integration constant using the initial conditions (ie the conditions we know to be true at t=0 - we usually know what these are), or the boundary conditions (ie the conditions we know to be true at x=0 and y=0).
What is involved in technology integration?
Technology Integration involves the incorporation of technological tools in educational areas. The usage of technology by students in aiding problem-solving is such an example.
What has the author John W Negele written?
John W. Negele has written: 'Quantum many-particle systems' -- subject(s): Degree of freedom, Functional Integration, Integration, Functional, Many-body problem, Quantum field theory, Quantum theory, Stochastic processes
How do you send fax to US with out using facebook?
Most fax machines have no integration with facebook, therefore there should be no problem sending a fax without it.
What is proactive communication?
Proactive community policing has a goal of problem solving. It emphasizes proactive enforcement proposing that street crimes can be reduced with greater community involvement and integration between citizens and police.
What cortex areas are involved with integration and memory?
The prefrontal cortex plays a role in integrating different types of information for decision-making and problem-solving. The hippocampus is essential for forming new memories and integrating them into existing knowledge networks in the brain.
What has the author Herbert M Voss written?
Herbert M. Voss has written: 'Application of numerical integration techniques to the low-aspect-ratio flutter problem in subsonic and supersonic flows' -- subject(s): Integral equations, Aerodynamic load, Flutter (Aerodynamics)
What has the author Harold Himsworth written?
Harold Himsworth has written: 'Lectures on the liver and its diseases' -- subject(s): Diseases, Liver 'The integration of medicine' 'Scientific knowledge & philosophic thought' -- subject(s): Methodology, Philosophy, Problem solving, Science, Theory of Knowledge
What are the principles of instruction?
The principles of instruction help to guide teachers. These principles are task/problem-centered, activation, demonstration, application, and integration. These five principles are broad so that instructors can make them their own and teach how they like while still falling within the guidelines.
What has the author V S Riabenkii written?
V. S. Riabenkii has written: 'Long-time numerical integration of the three-dimensional wave equation in the vicinity of a moving source' -- subject(s): Cauchy problem, Algorithms, Boundary conditions, Numerical integration, Three dimensional motion, Wave equations 'An application of the difference potentials method to solving external problems in CFD' -- subject(s): Computational fluid dynamics, Viscous flow, Boundary value problems, Compressible flow, Difference equations, Navier-Stokes equation
What is the value of the rate constant?
I depends on the problem. The rate constant is different depending on the problem in which it occurs.
