Question
Excercise 28 answer:
If x -1, let A(x) = -1g (1 + t2) dt A(x) represents the area of a region. Sketch that region. Use the result of Exercise 28 in Section 5.2 to find an expression for A(x). Find A'(x). What do you notice? If x 1 and h is a small positive number, then A(x + h) - A(x) represents the area of a region. Describe and sketch the region. Draw a rectangle that approximates the region in part (d). By comparing the areas of these two regions, show that A(x + h) - A(x)/h 1 + x2 Use part (e) to give an intuitive explanation for the result of part (c). Prove that ab x2 dx = b3 - a3/3 where Delta x = b - a/n, x1 = a + b - a/n, x2 = a + 2(b - a)/n, .... x1 = a + i(b - a)/n Thus,
Explanation / Answer
b) A(x) = x + 1 + [ x^3 + 1]/3 c) A'(x) = 1 + x^2
