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I know that ∫(a,b,f(x)dx = F(a) - F(b), so I was wondering if it's possible to define

*a*and

*b*so that the resulting definite integral equals the indefinite integral (where c = 0)

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- Thread starter Saracen Rue
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In summary, the conversation discusses the use of a calculator to sketch indefinite integrals and the possibility of defining a and b to equal the resulting definite integral with c = 0. The conversation also mentions that the sketch of a definite integral is the same as that of an indefinite integral with a zero integration constant, shifted downwards by G(a). It is suggested that setting a equal to the x-intercept of the indefinite integral of f(x) could result in a successful sketch.

- #1

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I know that ∫(a,b,f(x)dx = F(a) - F(b), so I was wondering if it's possible to define

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- #2

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$$F(x)=\int_a^x f(t)dt$$

then the sketch will be exactly the same as that of an indefinite integral ##G=\int f(x)dx## with zero integration constant, except shifted downwards by ##G(a)##.

- #3

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So if I makeandrewkirk said:

$$F(x)=\int_a^x f(t)dt$$

then the sketch will be exactly the same as that of an indefinite integral ##G=\int f(x)dx## with zero integration constant, except shifted downwards by ##G(a)##.

$$F(x)=\int_a^x f(t)dt$$

With no shift?

- #4

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Yes, that should work.

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Thank you! :)andrewkirk said:Yes, that should work.

A definite integral is a mathematical concept used to find the area under a curve between two specific points on a graph. It is represented by the symbol ∫ and has a lower and upper limit, such as ∫f(x)dx from a to b.

An indefinite integral is a mathematical concept used to find the general antiderivative of a function. It is represented by the symbol ∫ and does not have any limits, such as ∫f(x)dx.

A definite integral can be thought of as a special case of an indefinite integral, where the limits are specified. The definite integral is equal to the difference between the antiderivative evaluated at the upper limit and the antiderivative evaluated at the lower limit.

Understanding the difference between these two types of integrals is important for accurately calculating the area under a curve and for solving differential equations. It also allows for a better understanding of the fundamental theorem of calculus, which relates derivatives and integrals.

To determine if a definite integral is equal to an indefinite integral, you can evaluate the antiderivative at the upper and lower limits and see if the difference is equal to the definite integral. You can also use the fundamental theorem of calculus to calculate the definite integral directly from the function's antiderivative.

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