Q. 6 Fill in the blank: The length of... [FREE SOLUTION]

Chapter 6: Q. 6 (page 538)

Fill in the blank: The length of the graph of $y = x^{2}$ on $[2, 4]$ is equal to the area under the graph of the function ________ on the same interval.

Short Answer

Expert verified

The length of the graph of $y = x^{2}$ on [2, 4] is equal to the area under the graph of the function $\sqrt{1 + 4 x^{2}}$ on the same interval.

Step by step solution

Given

The given function is $y = x^{2}$ on the interval $[2, 4]$ .

To find

Fill in the blanks.

Calculation

Using derivative we get:

$y = x^{2} \frac{d y}{d x} = 2 x$

So the length of the arc is:

${鈭�}_{2}^{4} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x = {鈭�}_{2}^{4} \sqrt{1 + {(2 x)}^{2}} d x = {鈭�}_{2}^{4} \sqrt{1 + 4 x^{2}} d x$

Hence, the length of the graph of $y = x^{2}$ on [2, 4] is equal to the area under the graph of the function $\sqrt{1 + 4 x^{2}}$ on the same interval.

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91影视

Fill in the blank: The length of the graph of $y = x^{2}$ on $[2, 4]$ is equal to the area under the graph of the function ________ on the same interval.

Short Answer

Step by step solution

Given

To find

Calculation

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91影视

Fill in the blank: The length of the graph of y=x2on [2,4]is equal to the area under the graph of the function ________ on the same interval.

Short Answer

Step by step solution

Given

To find

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Statistics

Probability and Statistics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Fill in the blank: The length of the graph of $y = x^{2}$ on $[2, 4]$ is equal to the area under the graph of the function ________ on the same interval.