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Chapter 4: Q. 8 (page 372)

Why is it not necessary to write down an anti-derivative family when using the Fundamental Theorem of Calculus to calculate definite integrals? In other words, why don鈥檛 we have to use 鈥�+C鈥�?

Short Answer

Expert verified

It is not necessary to write down an anti-derivative family or "+C" when using the Fundamental Theorem of Calculus to calculate definite integrals is because it is a number having the exact value.

Step by step solution

01

Step 1. Given Information.

We have to state why do we not have to write "+C" when using the Fundamental Theorem of Calculus to calculate finite definite integrals.

02

Step 2. Reason.

In definite integral definite area is concerned with area under the graph and x-axis while the indefinite integrals is concerned with the anti-derivatives.

It is not necessary to write down an anti-derivative family or "+C" when using the Fundamental Theorem of Calculus to calculate definite integrals is because it is a number having the exact value.

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Most popular questions from this chapter

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

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

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.

Use a sentence to describe what the notation鈭�k=2100k means. (Hint: Start with 鈥淭he sum of....鈥�)

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�2xlnx-xlnx2dx.
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