# How do you evaluate the definite integral #int 8/(3+4x)# from #[0,1]#?

Therefore,

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To evaluate the definite integral ∫(8/(3+4x)) dx from 0 to 1, you can use the method of substitution. Let u = 3 + 4x, then du = 4 dx. Rearranging, dx = du/4. When x = 0, u = 3, and when x = 1, u = 7. The integral becomes ∫(8/u) * (1/4) du, which simplifies to (1/4) ∫(8/u) du. This integral is equal to (1/4) * 8 * ln|u| evaluated from 3 to 7. Substituting back in terms of x, this becomes (1/4) * 8 * [ln|7| - ln|3|], which simplifies to 2 * (ln(7/3)). Therefore, the value of the definite integral is 2 * ln(7/3).

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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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