Understanding "u" Substitution in Definite Integrals and the First Fundamental Theorem of Calculus
This guide explores the concept of "u" substitution in definite integrals and its application through the First Fundamental Theorem of Calculus. We'll break it down into two steps: first, finding the function F(x), and then determining its derivative F'(x). The theorem states that if f is continuous on the interval [a,b], then it is differentiable at every point in that interval. We also examine the effects of substitution on integration limits and provide several examples to clarify these concepts.
Understanding "u" Substitution in Definite Integrals and the First Fundamental Theorem of Calculus
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Presentation Transcript
Definite Integrals 5.6 “u” substitution
The First Fundamental Theorem of Calculus To understand this, lets do a problem in 2 steps: • Find F(x): • Find F’(x)
The First Fundamental Theorem of Calculus If f is continuous on [a,b] then is differentiable on every point in [a,b] and
u substitution We’ve talked about this a little; as you substitute “u” in, the limits of integration will change. Lets look at a few examples to see how these work:
Do you have to do this? No, you don’t. It just sometimes makes some very unwieldy problems look nicer and simplify quicker.
