# Chapter 7.3 Area and the Definite Integral Sep 4, 2019 7_02_08 PM.pdf

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I dy to a Indefinite Integral f oh I t Definite Integral Areae D LW O Tir D big Area under a curve I t DX b na_ Area of n rectangles fl x 10x t f x DX t t Xs DX t ft xn ox Short form if 1 xi OX As n X A x'Ix fix ox If Hx dx Exampts 1 Find the area under the curve Hx T h above the x axis from x l to x 5 using 4 rectangles ox I Likiniti 2 3 4 1 Right endpoints Area of rectangles LW f 2 I t f 3 I t t 14 Itf S I t T t'T t t 1.283
E left endpoints Area of rectangles IN th t f 121 t 431 t fly I t t t z t'T 2.083 2 Let f x 2 1 5 X O X a 2 X 4 ya i 6 04 2 a q flail DX 2 2101 5 2121 5 t12141 51 2161 5 be Write the definite integral that the sum approximates using left endpoints Area f O t th t f 4 12 a Definite integral to 12 5 dx n 4 L use a left lb right c average a b Id midpoints 3 FIX 2 1 5 from x 2 h x 4 ox I i S q A I f f 2 t fl 2 S t f 13 t f 3 S 21 units be A I f f 2 S t f 3 t f 13.5 tf 4 23 units 211