Home
Class 12
MATHS
Consider the two curves C(1):y=1+cos x a...

Consider the two curves `C_(1):y=1+cos x and C_(2): y=1 + cos (x-alpha)" for "alpha in (0,(pi)/(2))," where "x in [0,pi].` Also the area of the figure bounded by the curves `C_(1),C_(2), and x=0` is same as that of the figure bounded by `C_(2),y=1, and x=pi`.
For the values of `alpha`, the area bounded by `C_(1),C_(2),x=0 and x=pi` is

Text Solution

Verified by Experts

The correct Answer is:
1
`"Given that "D_(1)=D_(2)`
`overset(c)underset(1)int((1)/(x)-log x)dx=overset(a)underset(c)int(logx-(1)/(x))dx`
`((-1)/(x^(2))-x(logx-1))_(1)^(c)=(x(logx-1)+(1)/(x^(2)))_(c)^(a)`

`therefore" "0=a(log a-1)+(1)/(a^(2))`
`therefore" "a=1`
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

Consider the two curves C_(1):y=1+cos x and C_(2): y=1 + cos (x-alpha)" for "alpha in (0,(pi)/(2))," where "x in [0,pi]. Also the area of the figure bounded by the curves C_(1),C_(2), and x=0 is same as that of the figure bounded by C_(2),y=1, and x=pi . The value of alpha is

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

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

If A is the area bounded by the curves y=sqrt(1-x^2) and y=x^3-x , then of pi/Adot

The area of the region bounded by x^(2)+y^(2)-2x-3=0 and y=|x|+1 is

Find the area of the region bounded by the curves y=sqrt(x+2) and y=(1)/(x+1) between the lines x=0 and x=2.

Find the area of the region bounded by the curve C : y=tanx ,t a nge n td r a w ntoC at x=pi/4, and the x-axis.

Find the area bounded by y=cos x , the lines x=0 and x=2pi .