lecture33 - Lecture 33 1 Lecture 33: (Sec. 6.3, 6.4, 6.5)...

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Unformatted text preview: Lecture 33 1 Lecture 33: (Sec. 6.3, 6.4, 6.5) ex. Sketch the region corresponding to the follow- ing definite integral; then evaluate using geometric formulas. integraldisplay 2 (4- x ) dx Lecture 33 2 What if f ( x ) is negative for some x on [ a, b ]? Lecture 33 3 Section 6.4 Fundamental Theorm of Calculus To Evaluate integraldisplay b a f ( x ) dx ex. Find the area bounded by f ( x ) = 4 and the x- axis from x = a to x = b . What is the connection between the definite and in- definite integral? Lecture 33 4 We have the following result: Fundamental Theorem of Calculus Let f be continuous on [ a, b ] and let F be an an- tiderivative of f . Then integraldisplay b a f ( x ) dx = ex. Evaluate f ( x ) = integraldisplay 1 x 2 dx Lecture 33 5 ex. Evaluate integraldisplay ln2 ( e 2 x + 2) dx . Sketch the region represented by the integral. What is its area? 0.1 0.2 0.3 0.4 0.5 0.6 0.7 3.5 4.0 4.5 5.0 5.5 6.0 Lecture 33 6 Section 6.5 Substitution and the Definite Integral ex. Evaluate integraldisplay 1 (3 x- 2) 2 dx using substitution. Lecture 33 7 ex. Find the area of the region under the graph of y = ln( x 2 ) x from x = 1 to x = e . Lecture 33 8 ex. Evaluate integraldisplay 5 2 x x- 1 dx Lecture 33...
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lecture33 - Lecture 33 1 Lecture 33: (Sec. 6.3, 6.4, 6.5)...

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