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Chapter 4: Q. 63 (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.

鈭�05蟺/4|sinx|dx

Short Answer

Expert verified

The value of integral is 3-12and the plot is

Step by step solution

01

Step 1. Given information

An expression is given as鈭�05蟺/4|sinx|dx

02

Step 2. Evaluating integral

Simplify the integral as,

鈭�05蟺4|sinx|dx=鈭�0蟺2sinxdx+鈭�蟺2蟺-sinxdx+鈭�蟺5蟺4sinxdx=-cos蟺2+cos(0)+-cos(蟺)+cos蟺2+-cos5蟺4-cos(蟺)=0+1+1+0-12+1=3-12

And the plot is

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Most popular questions from this chapter

For each function f and interval [a, b] in Exercises 27鈥�33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.

f(x)=sin(x),[a,b]=[0,蟺], n = 3 with

a) Trapezoid sim b) Upper sum

For each function f and interval [a, b] in Exercises 27鈥�33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.

f(x)=x2,[a,b]=[0,3]left sum with

a) n = 3 b) n = 6

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

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

鈭�01鈥�11+x2dx

Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercises 21鈥�26, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].

f(x)=1-2x,[a,b]=[-3,1]
See all solutions

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