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Chapter 4: Q. 44 (page 373)

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�蟺/4蟺/2鈥�csc鈦�xcot鈦�xdx

Short Answer

Expert verified

Ans: The exact value of,鈭�蟺/4蟺/2鈥�csc鈦�xcot鈦�xdx=1-22

Step by step solution

01

Step 1. Given information.

given expression,

鈭�蟺/4蟺/2鈥�csc鈦�xcot鈦�xdx

02

Step 2. The objective is to determine the exact value of the definite integral.   

The exact value is calculated as shown below,

鈭�蟺4蟺2鈥�csc鈦�xcot鈦�xdx=[鈭�csc鈦�x]蟺4蟺2=鈭�csc鈦�蟺2+csc鈦�蟺4=鈭�1+12=1鈭�22

Therefore, the exact value is1-22.

03

Step 3. Check:

The required graph is,

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Most popular questions from this chapter

What is the difference between an antiderivative of a function and the indefinite integral of a function?

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Explain why the formula for the integral of xkdoes not

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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�(sec2x+csc2x)dx.
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