Chapter 4: Q. 32 (page 404)
Integral Formulas:
Fill in the blanks to complete each of the following integration formulas.
(The last six formulas involve hyperbolic functions and their inverses.)
Ans:
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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Prove Theorem 4.13(c): For any real numbers a and b, Use the proof of Theorem 4.13(a) as a guide.
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?
Given formula for the areas of each of the following geometric figures
a) area of circle with radius r
b) a semicircle of radius r
c) a right triangle with legs of lengths a and b
d) a triangle with base b and altitude h
e) a rectangle with sides of lengths w and l
f) a trapezoid with width w and height
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
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