Question: Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph

the graph using first two and then four rectangles. f(x) = x3

$between x = O and x = 2 \\3 n n S$

ak =6 and _ by = 42, find the following values. k

1 K = 14 The functions f and g are integrable and

Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two and then four rectangles. f(x) = x3 between x = O and x = 2 \\3 n n S ak =6 and _ by = 42, find the following values. k = 1 k = 1 n n bk n n n 5ak. E 42 2 (ak + bk), _ (ak- bk), Z (bK - Gak) k = 1 K = 1 K = 1 k = 1 K = 14 The functions f and g are integrable and f(x)dx = 4, f(x)dx = - 4, and g(x)dx =6. Use these to complete parts (a) through (f). 2 . . . 4 a. J f( x ) dx = 0 3 4 ( Simplify your answer.) 2 b. g(x)dx = 7 (Simplify your answer.)8 9 Suppose that f is integrable, and that If(z)dz = 3 and If(z)dz = 6. Find the value of the following definite integrals. m 9 (a) If(z)dz = E (Type an integer or a decimal.) 8 \fUse a definite integral to find the area of the region between the given curve and the x-axis on the interval [0, b]. y = 11x2 [0) The area is D. b What values of a and b maximize the value of [(12x - x2) dx? a (Hint: Where is the integrand positive?) 7 a = D and b = D maximize the given integral. (Simplify your answer. Type a whole number.)

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