Chain rule for integral
[DOCX File]MA-C4 Integral calculus-y12
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The reverse chain rule cannot be applied to any other expressions of x , i.e. the reverse chain rule cannot be applied to f a x 2 + b . dx as the expression of x is not linear. Challenge students to develop a solution to an integral of the form (3 x -2) 5 . dx
[DOC File]Integration by Substitution
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Recall from Chapter 2 that if is a differentiable function of and if is a real number and then the Chain Rule tells us that . The reverse of this formula is the integration formula, Sometimes it is not easy to integrate directly. For example, look at this integral: One way to integrate is to first expand the integrand and then integrate term by ...
[DOC File]Section 1
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Definite Integral. The definite integral is an integral of the form. ... Recall that the chain rule of differentiation was used to differentiate a composition of two functions. The formula for the chain rule was given by: Chain Rule of Differentiation. Suppose we let and let . Then and hence
[DOC File]Definition (Definite Integral): Let be continuous on the ...
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Leibniz Integral Rule. Proof: By the First FTIC and the Chain Rule, we have (Let Then on Zero Rule. Proof: The “if part” is trivial. Therefore, we shall only prove the “only if” part. So, assume that Since Now, by continuity. (U-Substitution Rule. Proof: Let Then, Thus,. ( Change of Variable Rule. Proof: Let Then, (
[DOC File]Chapter 3
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Find the indefinite integral. Solution ( (Example 8.6. Find f(x) given if . Solution ( First find. Since , we get , so . (8.2 Integration using substitution. For differentiation we had special rules like chain rule, product rule, and quotient rule.
[DOCX File]Teaching objectives
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Find the area between 2 curves including choosing the appropriate method of integration
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