# How do you evaluate the definite integral #int 4x-5# from #[1,2]#?

Recall the Fundamental Principle of Definite Integration :

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To evaluate the definite integral ∫(4x - 5) dx from 1 to 2, you first find the antiderivative of the integrand, which is (2x^2 - 5x). Then, you evaluate this antiderivative at the upper and lower limits of integration and subtract the value at the lower limit from the value at the upper limit. So, you have:

[ (2(2)^2 - 5(2)) ] - [ (2(1)^2 - 5(1)) ] = [ (8 - 10) ] - [ (2 - 5) ] = [ (8 - 10) ] - [ -3 ] = -2 + 3 = 1

Therefore, the value of the definite integral ∫(4x - 5) dx from 1 to 2 is 1.

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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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