What are five basic properties of definite integrals?

Answer 1

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#int_a^a f(x) dx=0#
#int_a^b f(x) dx=-int_b^a f(x) dx#
#int_a^b [f(x)+g(x)]dx=int_a^b f(x) dx+int_a^b g(x) dx#
#int_a^b k f(x)dx=k int_a^b f(x) dx#
#int_a^b f(x) dx=int_a^c f(x) dx + int_c^b f(x) dx#

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Answer 2

The five basic properties of definite integrals are:

  1. Linearity: The integral of a sum is the sum of the integrals.
  2. Constant multiple: The integral of a constant times a function is the constant times the integral of the function.
  3. Interval addition: Integrating over the union of two intervals is the sum of the integrals over each interval separately.
  4. Reversing limits: Reversing the limits of integration changes the sign of the integral.
  5. Integrating the zero function: The integral of the zero function over any interval is zero.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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