Home
Class 12
MATHS
If ' a^(prime)(a >0) is the value of par...

If `' a^(prime)(a >0)` is the value of parameter for each of which the area of the figure bounded by the straight line `y=(a^2-a x)/(1+a^4)` and the parabola `y=(x^2+2a x+3a^2)/(1+a^4)` is the greatest, then the value of `a^4` is___

Text Solution

Verified by Experts

The correct Answer is:
3
`y=(a^(2)-ax)/(1+a^(4))" (1)"`
`=(x^(2)+2ax+3a^(2))/(1+a^(4))c" (2)"`
Point of intersection of (1) and (2)
`(a^(2)-ax)/(1+a^(4))=(x^(2)+2ax+3a^(2))/(1+a^(4))`
`(x+a)(x+2a)=0`
`x=-a,-2a`
`"Req. area "=overset(-a)underset(-2a)int[((a^(2)-ax)/(1+a^(4)))-((x^(2)+2ax+3a^(2))/(1+a^(4)))]`
`therefore" "f(a)=(a^(3))/(6(1+a^(4)))`
If f(a) is max, then f'(a)=0
`rArr" "3+3a^(4)-4a^(4)=0`
`"or "a^(4)=3`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise JEE Main Previous Year|10 Videos

  • AREA

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

  • AREA

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE|Exercise Question Bank|29 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If 'a'(a>0) is the value of parameter for each of which the area of the figure bounded by the straight line y=(a^(2)-ax)/(1+a^(4)) and the parabola y=(x^(2)+2ax+3a^(2))/(1+a^(4)) is the greatest,then the value of a^(4) is _(-)

Compute the area of the figure bounded by the straight lines =0,x=2 and the curves y=2^(x),y=2x-x^(2)

What is the area of the parabola x^(2)=y bounded by the line y=1?

Find the area of the figure bounded by the parabolas x=-2y^(2),x=1-3y^(2)

The area of the region bounded by the lines y=2x+1y=3x+1 and x=4 is

Find the area of the region bounded by the parabola y^(2)=2x and straight line x-y=4 .