Question

Use finite approximation to estimate the area under the graph of f(x) = 9x? and above the graph of f(x) = O from xo + 0 to x = 4 using i) a lower sum with two rectangles of equal width ii) a lower sum with four rectangles of equal width ii) an upper sum with two rectangles of equal width. iv) an upper sum with four rectangles of equal width. The estimated area using a lower sum with two rectangles of equal width is II square units. (Simplify your answer. Type an integer or a decimal.) The estimated area using a lower sum with four rectangles of equal width is square units (Simplify your answer. Type an integer or a decimal.) The estimated area using an upper sum with two rectangles of equal width is square units. (Simplify your answer. Type an integer or a decimal.) The estimated area using an upper sum with four rectangles of equal width is square units. (Simplify vour answer. Type an integer or a decimal.)

Answer 1

Sol. Here f(x) = 9x?, 90 = 0, bo=4 when n=2, AX- b-a . 4-0 = 2 Intervals are ba [0,2], [2,4) 0x [f(0) + F(2)] 2 [0+36] CO Lower Sum = Lower Sum - 72 Ubber sum = 1x [F(9) + f(43) 2[36+ 144] = =360 When n=u 12 9 bo-do 4-0 4 = 1 n Intervals ii) Lower um = are [0,1],[1,2],[2, 3], [3,4] Ax [f(0) + f(n+ f (2) + f(3)] [0+ 9+ 36+81] - 126 (iv) Ubber suma 1x [ f(1) + F(2) + f(3) + f(4)] [9+36+81 +144] 970 CS Scanned with CamScanner