CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Area of a Circle

The area in s...

Question

The area (in sq. units) of the region, given by the set ${(x, y) \in R \times R | x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x}$ is

A

\frac{8}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{7}{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

\frac{17}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{13}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{7}{3}$

Area $A = \int_{0}^{1} ((4 - 2 x) - 2 x^{2}) d x$
$= {[4 x - x^{2} - \frac{2 x^{3}}{3}]}_{0}^{2} = 4 - 1 - \frac{2}{3} = \frac{7}{3}$

Suggest Corrections

thumbs-up

3

Similar questions

Q. The area (in sq. units) bounded by the curves

C_{1} : y = 2 x - x^{2}, x \in R

C_{2} : y = tan (\frac{π}{4} x), x \in [0, 2)

Q. The area (in sq. units) of the region

{x \in R : x \geq, y \geq 0, y \geq x - 2

y \leq \sqrt{x}}

A = {(x, y) \in R \times R | 2 x^{2} + 2 y^{2} - 2 x - 2 y = 1},

B = {(x, y) \in R \times R | 4 x^{2} + 4 y^{2} - 16 y + 7 = 0}

C = {(x, y) \in R \times R | x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}

.
Then the minimum value of

| r |

A \cup B \subseteq C

Q. The area (in sq. units) of the region described by

A = {(x, y) | y \geq x^{2} - 5 x + 4, x + y \geq 1, y \leq 0}

Q. Area of the region bounded by

y = e^{x}, y = e^{- x}, x = 0

x = 1

in sq. units is:

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Area of a Circle

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon