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Finding antiderivatives essentially involves "un-doing" the derivative. If the function you are antidifferentiating involves variables raised to a power, instead of multiplying by the power and decreasing the degree by one as you would do when taking the derivative, you add one to the degree of the power and multiply by the reciprocal of the new power .
For example, if the function you are antidifferentiating is x^2, you add one to the power (so now it is x^3) and multiply by the power's reciprocal (1/3). The antiderivative is (1/3)x^(3) plus an arbitrary constant.
If the function you are antidifferentiating involves sin and cos functions, use trig identities, partial fractions, u substitution, etc. Remember that you can always take the derivative of the expression you find as the antiderivative to verify its validity.
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Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What do integrate mean?
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.
What are the different uses of integration calculator?
Integral calculators calculate definite and indefinite integrals (antiderivatives) for use in calculus, trigonometry, and other mathematical fields/formulations.
How can you write a function that represents all possible antiderivatives of a given function?
Given a function f(x) find any anti-derivative, F(x). The set of all possible derivatives is obtained by adding a term not involving x which can take any value. So F(x) + C is a general derivative, where C can take any value.
How is calculus connected to foods?
Well, you can use antiderivatives to find the volume of a pear or ring donut, by rotating a curve (or 2 for the donut) about a line. You can have problems stating how many french fries are produced at an amusement park and how many are eaten per hour, and figure out the average rate that they are eaten, or the instantaneous rate at a given time (most likely higher around lunch and dinner times rather than when the park first opens) using derivatives.
Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What integrated mean'?
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.
What do integrate mean?
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.
What are the different uses of integration calculator?
Integral calculators calculate definite and indefinite integrals (antiderivatives) for use in calculus, trigonometry, and other mathematical fields/formulations.
How can you write a function that represents all possible antiderivatives of a given function?
Given a function f(x) find any anti-derivative, F(x). The set of all possible derivatives is obtained by adding a term not involving x which can take any value. So F(x) + C is a general derivative, where C can take any value.
Can a function have more than one antiderivative?
yes, look at the function f(x)=3x^2 The antiderivative is x^3+C where C is the constant and is more than one value for C. In fact, 3x^2 will have an infinite number of antiderivatives.
How is calculus connected to foods?
Well, you can use antiderivatives to find the volume of a pear or ring donut, by rotating a curve (or 2 for the donut) about a line. You can have problems stating how many french fries are produced at an amusement park and how many are eaten per hour, and figure out the average rate that they are eaten, or the instantaneous rate at a given time (most likely higher around lunch and dinner times rather than when the park first opens) using derivatives.
How is integration through substitution related to the Chain Rule?
i love wikipedia!According to wiki: In calculus, integration by substitution is a method for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool for mathematicians. It is the counterpart to the chain rule of differentiation.
When you find particular integral then why you not add constantof integration?
Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration. Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration: (1 + C) - (0 + C) = 1 The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
What is the integral of 1 plus sin2xcscx?
The indefinite integral with respect to x (assumed that, for future reference you should always list the variable of integration (dx, dy, dz, dq, dt, etc...)) of: f(x)=1+sin2(x)csc(x) csc(x) is the same as 1/sin(x), and sin2(x)/sin(x)=sin(x), so f(x) can be simplified to: f(x)=1+sin(x) the antiderivatives of both of the components of this function are easy and known. Since they are added together and not multiplied or divided, they can be and integrated individually and then added together in the end (capital-letter function names denote antiderivatives): f(x)=h1(x)+h2(x) h1(x)=1 h2(x)=sin(x) H1(x)=x+C H2(x)=-cos(x)+C F(x)=H1(x)+H2(x) F(x)=x-cos(x)+C
What is the connection between anti-derivatives and definite integrals?
Definite integrals are definite because the limits of integration are prescribed. It is also the area enclosed by the curve and the ordinates corresponding to the two limits of integration. Antiderivatives are inverse functios of derivatives. If the limits of the integral are dropped then the integration gives antiderivative. Example Definite integral of x with respect to x between the value of x squared divided by 2 between the limits 0 and 1 is 1/2. Antiderivative of x is x squared divided by two.
Could Give and explain the two basic classifications of calculus?
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.
