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Chapter 4: Q. 4 (page 375)

Use the Fundamental Theorem of Calculus to find an equation for A(x) that does not involve an integral.

Short Answer

Expert verified

A(x)鈮�鈭�nf1x1x

Step by step solution

01

Step 1. Given information is:

Suppose A(x) is a function that for each x>0 is equal to area under the graph of f(t)=t2 from 0 to x.

02

Step 2. Determining A(x)

Theareaunderthecurveisgivenby:A(x)=f1x1x+f1x1x+.....+f1x1xA(x)鈮�鈭�nf1x1xThus,A(x)鈮�鈭�nf1x1x

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Most popular questions from this chapter

Shade in the regions between the two functions shown here on the intervals (a) [鈭�2, 3]; (b) [鈭�1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?

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. (Hint for Exercise 54: tanx=sinxcosx).

鈭�e3x-2e4xe2xdx.

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn鈫�鈭�鈭�k=1nk+12n3-1

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2, and 鈭�36g(x)dx=3, then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�-2-2x(f(x)+3)2dx

Verify that鈭�cotxdx=ln(sinx)+C. (Do not try to solve the integral from scratch.)
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