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Chapter 4: Q. 4 (page 327)

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

Short Answer

Expert verified

The area in between the function is approximately 16 sq.units

Step by step solution

01

Given information

We are given a functionf(x)=x2

02

plot the graph of the function

We get,

03

Now using rectangle find the area

We get,

And also

Hence total area can be given as

3+6+5+2=16sq.units

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Most popular questions from this chapter

Verify that鈭�lnxdx=x(lnx-1)+C(Do not try to solve the integral from scratch.

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The absolute area between the graph of f and the x-axis on [a, b] is equal to|鈭�abf(x)dx|.

(b) True or False: The area of the region between f(x) = x 鈭� 4 and g(x) = -x2on the interval [鈭�3, 3] is negative.

(c) True or False: The signed area between the graph of f on [a, b] is always less than or equal to the absolute area on the same interval.

(d) True or False: The area between any two graphs f and g on an interval [a, b] is given by 鈭�ab(f(x)-g(x))dx.

(e) True or False: The average value of the function f(x) = x2-3 on [2, 6] is

f(6)+f(2)2= 33+12= 17.

(f) True or False: The average value of the function f(x) = x2-3on [2, 6] is f(6)-f(2)4= 33-14= 8.

(g) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 2] and the average value of f on [2, 5].

(h) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 3] and the average value of f on [3, 5].

Consider the sequence A(1), A(2), A(3),.....,A(n) write our the sequence up to n. What do you notice?

Explain why we call the collection of antiderivatives of a function f a family. How are the antiderivatives of a function related?

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�24x2+1dx
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