Chapter 4: Q. 12 (page 351)
Use graphs to determine whether each of the following definite integrals is equal to a positive number, a negative number, or zero:
Short Answer
The definite integral is zero.
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Chapter 4: Q. 12 (page 351)
Use graphs to determine whether each of the following definite integrals is equal to a positive number, a negative number, or zero:
The definite integral is zero.
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Use a sentence to describe what the notation means. (Hint: Start with 鈥淭he sum of....鈥)
Suppose on [1, 3] and on (鈭掆垶, 1] and [3,鈭). Write the area of the region between the graphs of f and g on [鈭2, 5] in terms of definite integrals without using absolute values .
Use integration formulas to solve each integral in Exercises 21鈥62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating
.
Approximations and limits: Describe in your own words how the slope of a tangent line can be approximated by the slope of a nearby secant line. Then describe how the derivative of a function at a point is defined as a limit of slopes of secant lines. What is the approximation/limit situation described in this section?
Explain why it would be difficult to write the sum in sigma notation.
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