Home
Class 12
MATHS
The value of a(agt0) for which the area ...

The value of `a(agt0)` for which the area bounded by the curves `y=(x)/(6)+(1)/(x^(2)),y=0,x=a, and x=2a` has the least value is ___.

Text Solution

Verified by Experts

The correct Answer is:
1
`f(a)=overset(2a)underset(a)int((x)/(6)+(1)/(x^(2)))dx=((x^(2))/(12)-(1)/(x))_(a)^(2a)`
`=((4a^(2))/(12)-(1)/(2a)-(a^(2))/(12)+(1)/(a))=(a^(2))/(4)+(1)/(2a)`
`"Let "f'(a)=(2a)/(4)-(1)/(2a^(2))=0`
`rArr" "a=1` which is point of minima.
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 Subjective Type|2 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

Similar Questions

Explore conceptually related problems

Find the area bounded by the curve x=7 -6y-y^2 .

Find the area bounded by the curves y=x^(3)-x and y=x^(2)+x.

Find the area bounded by the curves x+2|y|=1 and x=0 .

The area bounded by the curve y=3/|x| and y+|2-x|=2 is

The area bounded by the curve a^(2)y=x^(2)(x+a) and the x-axis is

Find the area bounded by the curves (x -1)^(2) + y^(2) = 1 and x^(2) + y^(2) = 1 .

Find the area bounded by the curve x^2=y ,x^2=-ya n dy^2=4x-3

Find the area bounded by the curves x^2+y^2=4, x^2=-sqrt2 y and x=y

Find the area bounded by curves {(x,y): y ge x^(2) and y = |x|}

Find the area of the region bounded by the curves y = x^(2) + 2, y = x, x = 0 and x = 3.