Area using n rectangles! How wide is each rectangle? y = x2 How do we find each rectangles height?"too big" area =
Area using n rectangles! y = x2 fundamental idea: to get the area, we . . . . Or, we could just do . . . . .
Integral Notation and Areas Area = rectangle 1 + rectangle 2 + . . . . + rectangle n y = f (x) x1 x2 x3 a b One restriction: This works if, and only if, . . . . . .n rectangles, each with width = ∆x and height = f (xi) a b
Find the area of the region bounded by y = x2 +1 and the x-axis from x = 1 to x = 3. 1) Using an integral by hand: 2) By graphing the curve on your grapher, and looking at the 2nd Trace menu! 3) Using Math #9: fnInt on your calculator.
Find the area between each graph and the x-axis. 1) 2) (why is the answer not area = ?)
Find the shaded area. 5) 6) π 7) a b
Homework p. 679 2, 3, 7 "Use the Fundamental Theorem" means p. 661 2 "use definite integrals and antiderivatives". p. 647 1, 2 Next week: More applications of integrals. Test: Monday, Nov. 21