Chapter 4: Q. 4 (page 384)

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = $\frac{1}{2}$ on $[- \frac{π}{2}, 2 π]$ ?

Short Answer

Expert verified

three

Step by step solution

Step1. Given Information

$The functions are,$

$f (x) = \sin x; g (x) = \frac{1}{2}$

$The objective is to determine the number of definite integrals would require in order to calculate$

$the absolute area between f (x) = \sin x and g (x) = \frac{1}{2} on [- \frac{π}{2}, 2 π] .$

Step2. Consider, the following graph

Step3. Answer

From the above figure it is clear that 3 intervals are required to calculate the absolute area between $f (x) = \sin x$ and $g (x) = \frac{1}{2}$ on $[- \frac{π}{2}, 2 π]$

1st inteval from role="math" localid="1649148607017" $[- \frac{π}{2}, 0]$

2nd interval $[0, π]$

3rd interval $[π, 2 π]$

Therefore, the answer is three.

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Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = $\frac{1}{2}$ on $[- \frac{π}{2}, 2 π]$ ?

Short Answer

Step by step solution

Step1. Given Information

Step2. Consider, the following graph

Step3. Answer

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Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = 12on [-π2,2π] ?

Short Answer

Step by step solution

Step1. Given Information

Step2. Consider, the following graph

Step3. Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = $\frac{1}{2}$ on $[- \frac{π}{2}, 2 π]$ ?