MAT 21B Lecture 9: MAT 21B – Lecture 9 – Application of Definite Integrals in Area Under a Curve

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21B
• Professor: David Cherney

Document Summary

Additionally, you drove 50 miles/hour the next hour. We can think of this as a function of velocity, v(t) = {(cid:888)(cid:882)(cid:3040)(cid:3039)(cid:3046) Thus, the total distance traveled is (cid:1874)(cid:4666)(cid:1872)(cid:4667)(cid:1856)(cid:1872)= (cid:888)(cid:882) (cid:3040)(cid:3039)(cid:3046) We are more concerned with happens within the time interval. For example if v(t) is in: example: (cid:1874)(cid:4666)(cid:1872)(cid:4667) (cid:3029)(cid:3028) feet/second, then dt is in seconds. (cid:1876)(cid:4666)(cid:1854)(cid:4667) (cid:1876)(cid:4666)(cid:1853)(cid:4667) is in feet, calculate the area of the rectangle with a base of 2 inches and a height of 5 meters. 0 and on the right by x = 2: a) without the ftoc (cid:2870) (cid:2868) =lim (cid:4666)(cid:2870)(cid:1863)(cid:4667)(cid:2870) lim [(cid:4666)(cid:882)+(cid:2870) (cid:2868) (cid:1863)(cid:4667)(cid:2870)] (cid:2870)= (cid:3038)=(cid:2869) (cid:3038)=(cid:2869) lim (cid:2870)=lim . Using vertical strips, we obtain the area equal to: b) with the ftoc, example 2: calculate the area of the shape formed between the graphs of cos(x) and sin(cid:894)x(cid:895) on [0, ]. cos(cid:4666)(cid:1876)(cid:4667) sin(cid:4666)(cid:1876)(cid:4667)(cid:1856)(cid:1876)+ sin(cid:4666)(cid:1876)(cid:4667) cos(cid:4666)(cid:1876)(cid:4667)(cid:1856)(cid:1876)= [sin(cid:4666)(cid:1876)(cid:4667)+cos (cid:4666)(cid:1876)(cid:4667)](cid:2868)/(cid:2872)