SECTION 6.2 Integration by Substitution. U-SUBSTITUTION.

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Presentation transcript:

SECTION 6.2 Integration by Substitution

U-SUBSTITUTION

USING THE SUBSTITUTION METHOD

EXAMPLE

WHAT IF THERE IS A CONSTANT LEFT OVER?

METHOD 2: “BEACH BOYS”

ADDITIONAL EXAMPLES

USING TRIG IDENTITIES

DO-NOW: HOMEWORK QUIZ  Suppose that a point moves along some unknown curve y = f(x) in the xy-plane in such a way that at each point (x, y) on the curve, the tangent line has a slope x 2. Find an equation for the curve given that it passes through the point (2, 1).

U-SUBSTITUTION IN DEFINITE INTEGRALS  Two methods for calculating the definite integral:  1. Perform the u-substitution, integrate, substitute back in for u, and evaluate at the given limits of integration.  2. Perform the u-substitution, integrate, change the limits of integration from x to u, and evaluate the function of u at the new limits of integration.

EXAMPLE

ADDITIONAL EXAMPLES

AP MC PRACTICE

MORE AP MC PRACTICE

DO-NOW: HOMEWORK QUIZ

SEPARABLE DIFFERENTIAL EQUATIONS

EXAMPLES