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Chapter 4: Q. 38 (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�0蟺鈥�sin2鈦�x+cos2鈦�xdx

Short Answer

Expert verified

Ans: The exact value is,鈭�0蟺鈥�sin2鈦�x+cos2鈦�xdx=蟺.

Step by step solution

01

Step 1. Given information.

given expression,

鈭�0蟺鈥�sin2鈦�x+cos2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�0蟺鈥�sin2鈦�x+cos2鈦�xdx=鈭�0蟺鈥�1dxsin2鈦�x+cos2鈦�x=1=[x]0蟺=蟺 Therefore, the exact value is 蟺.
03

Step 3. Check 

The required graph is,

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Most popular questions from this chapter

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

鈭�x3+42dx.

Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on [-蟺2,2蟺]?

Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?

Approximate the same area as earlier but this time with eight rectangles is this over approximation or under approximation of the exact area under the graph

Given a simple proof that鈭�k=5n(ak+bk)=鈭�k=5nak+鈭�k=5nbk

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�04(2x-3)2+5dx
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