Home
Class 12
MATHS
Let g(x)=cos^2 x,f(x)=sqrtx and alpha,be...

Let g(x)=cos^2 x,f(x)=sqrtx and alpha,beta (alpha

A

` (1)/(2)(sqrt(3)-1)`

B

` (1)/(2)(sqrt(3)+1)`

C

` (1)/(2)(sqrt(3)-sqrt(2))`

D

` (1)/(2)(sqrt(2)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
` rArr 18x^(2)-9pix +pi^(2)=0 `
` rArr 18x^(2)-6pi x-3pix +pi^(2)=0 `
` (6x-pi)(3x-pi )=0 `
`rArr x=(pi)/(6),(pi)/(3) `
` " Now, " alpha lt beta " " alpha=(pi)/(6), `
` beta=(pi)/(3)`
` "Given, " g(x)=cosx^(2) " and " f(x)=sqrt(x) `
` y= gof(x) `
` therefore y=g(f(x))=cosx `
Area of region bounded by ` x= alpha, x= beta , y=0 ` and curve ` y=g(f(x)) ` is
`A=int_(pi//6)^(pi//3) cosx dx `
` A=[sinx]_(pi//6)^(pi//3) `
`A="sin"(pi)/(3)-"sin"(pi)/(6)=(sqrt(3))/(2)-(1)/(2)`
` A=((sqrt(3)-1)/(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) :R->R,f(x)={(2x+alpha^2,xge2),((alpha x)/2+10,x lt 2)) If f(x) is onto function then alpha belongs to (A) [1,4] (B) [-2,3] (C) [0,3] (D) [2,5]

Let f(x) = ax^(2) + bx + c, a != 0 and Delta = b^(2) - 4ac . If alpha + beta, alpha^(2) + beta^(2) and alpha^(3) + beta^(3) are in GP, then

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha and beta are the roots of 2x^2-5x+3=0 form the equation whose roots are alpha+beta and 1/alpha+1/beta

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.

If alpha,beta(alpha < beta) are the roots of equation 6x^2+11="" x+3="0 , then which following real? (a) cos^(-1)alpha (b) sin^(-1)beta (c) cosec^(-1)alpha (d) both cot^(-1)alpha and cot^(-1)beta