Home
Class 12
MATHS
Find the smallest area bounded by the cu...

Find the smallest area bounded by the curves `y=x-sin x, y= x+ cos x.`

Text Solution

Verified by Experts

The correct Answer is:
`2sqrt(2)` sq. units
Solving given curves, we have x-sin x = x + cos x
`therefore" tan x =-1`
For smallest bounded area we must consider two consecutive solutions,
`i.e.," "x=-(pi)/(4),(3pi)/(4)`
`therefore" Required area "=|overset(3pi//4)underset(-pi//4)int[(x + cos x)-(x- sin x)]dx |`
`=|overset(3pi//4)underset(-pi//4)int[cos x + sin x] dx |`
`=[sin x - cos x ]_(-pi//4)^(3pi//4)`
`=((1)/(sqrt(2))+(1)/(sqrt(2)))-(-(1)/(sqrt(2))-(1)/(sqrt(2)))`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the area bounded by the curves y = sin x, y = cos x between x axis, x = 0 and x = (pi)/(2)

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

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

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

Find the area bounded by x=2y-y^2

Find the area bounded by the curve y = sin x between x = 0 and x = 2pi .

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

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