Chapter 5: Q17P (page 257)

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The area under the curve.

Short Answer

Expert verified

The area under the curve is obtained as $A = \frac{4 \sqrt{2}}{3}$ units.

Step by step solution

Step 1: Definition of Area under the curve

The region is circumscribed by the function that is dealing with. In this, vertical lines denote the function's boundaries, and the x-axis is known as the area under the curve.

Representation of the area bounded by the curve

Draw the bounded region for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ .

Determination of area of the curve

Determine the value of area of curve.

$A = \int_{0}^{2} \sqrt{x} d x = {\frac{x^{1 + \frac{1}{2}}}{1 + \frac{1}{2}}}_{0}^{2} n = \frac{2}{3} {[x^{\frac{3}{2}}]}_{0}^{2}$

Thus, the area under the curve is obtained as

A = \frac{4 \sqrt{2}}{3}

units.

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In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The area under the curve.

Short Answer

Step by step solution

Step 1: Definition of Area under the curve

Representation of the area bounded by the curve

Determination of area of the curve

One App. One Place for Learning.

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In Problems 17 to 30, for the curve y=x, between x=0and x=2,find:The area under the curve.

Short Answer

Step by step solution

Step 1: Definition of Area under the curve

Representation of the area bounded by the curve

Determination of area of the curve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Magnetism and Electromagnetic Induction

Electric Charge Field and Potential

Astrophysics

Medical Physics

Solid State Physics

Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The area under the curve.