# How do you change bounds when you integrate by substitution method?

Use the substitution you made and arithmetic.

With these substitutions, we now need to find:

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When you use the substitution method to integrate a function, you need to change the bounds of integration to match the new variable.

Suppose you have an integral of the form ( \int_{a}^{b} f(u) , du ), where ( u = g(x) ) is the substitution. After making the substitution, you change the bounds to match the new variable ( u ). The new lower bound is ( g(a) ) and the new upper bound is ( g(b) ).

So, if you have ( \int_{a}^{b} f(u) , du ) and you substitute ( u = g(x) ), the integral becomes ( \int_{g(a)}^{g(b)} f(u) , du ).

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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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