Home
Class 12
MATHS
Find the area enclosed by the figure des...

Find the area enclosed by the figure described by the equation `x^(4)+1=2x^(2)+y^(2).`

Text Solution

Verified by Experts

The correct Answer is:
`(8)/(3)` sq. units
`x^(4)+1=2x^(2)+y^(2)`
`therefore" "x^(4)-2x^(2)+1=y^(2)`
`therefore" "(x^(2)-1)^(2)=y^(2)`
`therefore" "y=pm(x^(2)-1),` which are two parabolas.

`"Required area "A=4overset(1)underset(0)int(1-x^(2))dx`
`=4[x-(x^(3))/(3)]_(0)^(1)=(8)/(3)` sq. units.
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE ENGLISH|Exercise Concept Application Exercise 9.3|7 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Exercises - Single Correct Answer Type|40 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Concept Application Exercise 9.1|9 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE ENGLISH|Exercise Comprehension Type|5 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

Similar Questions

Explore conceptually related problems

Find the area enclosed by the circle x^2+y^2=a^2 .

Find the area enclosed by the curves x^2=y , y=x+2,

Find area enclosed by |x|+|y|=1 .

Find the area enclosed by the curves y=4x^2 and y^2=2x .

Find the area enclosed by the curves max(2|x|,2|y|)=1

Find the area enclosed by the curve y=3x and y=6x- x^(2)

Find the area of the figure, bounded by the graph functions y x^2 and y=2x-x^2

Find area enclosed by |y|=1-x^(2) .

Find the area enclosed by the curves x^2=y , y=x+2 and x-axis

The area enclosed by the curve y^2 +x^4=x^2 is