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Chapter 4: Q. 6 (page 351)

Explain geometrically what the definition of the definite integral as a limit of Riemann sums represents. Include a labeled picture of a Riemann sum (for a particular n) that illustrates the roles of n, x, 鈭�x, xk*and f(x*k). What happens in the picture as n 鈫� 鈭�?

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Most popular questions from this chapter

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = 12on [-蟺2,2蟺] ?

Prove that 鈭�13(3x+4)dx=20in three different ways:

(a) algebraically, by calculating a limit of Riemann sums;

(b) geometrically, by recognizing the region in question as a trapezoid and calculating its area;

(c) with formulas, by using properties and formulas of definite integrals.

Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.

鈭�04(2x-3)2+5dx

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�0蟺鈥�sin2鈦�x+cos2鈦�xdx

Approximate the area between the graph f(x)=x2and the x-axis from x=0 to x=4 by using four rectangles include the picture of the rectangle you are using
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