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Chapter 4: Q. 50 (page 373)

Use the Fundamental Theorem of Calculus to find the exact

values of each of the definite integrals in Exercises 19鈥�64. Use

a graph to check your answer. (Hint: The integrands that involve

absolute values will have to be considered piecewise.)

鈭�041(2x+1)52dx

Short Answer

Expert verified

鈭�041(2x+1)52dx=2681.

Step by step solution

01

Step 1. Given information.

A definite integral is given as鈭�041(2x+1)52dx.

02

Step 2. Using the Fundamental theorem of Calculus.

We get

鈭�041(2x+1)52dx=鈭�04(2x+1)-52dx=12[(2x+1)-52+1-52+1]04=12[(2x+1)-32-32]04=12(-23)[1(2x+1)32]04=-13(1932-1)=-13(127-1)=-13(-2627)=2681

So the exact value of the given definite integral is2681.

03

Step 3. The graph to verify the answer is

The solution is area under graph which is

a鈮�0.320987鈮�2681

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Most popular questions from this chapter

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

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 heighth1,h2

Fill in each of the blanks:

(a) 鈭�x6dx=+C.

(b) is an antiderivative of role="math" localid="1648619282178" x6.

(c) The derivative of is x6.

Write out all the integration formulas and rules that we know at this point.

Explain why the formula for the integral of xkdoes not

apply whenk=-1. What is the integral of x-1?
See all solutions

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