Let g(x) = cos x², f(x) = $\sqrt{x}$ and $α, β (α < β)$ be the roots of the quadrtic equation 18x² - 9πx + π² = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0 is

$\frac{1}{2} (\sqrt{2 - 1})$

$\frac{1}{2} (\sqrt{3 - 1})$

$\frac{1}{2} (\sqrt{3 + 1})$

$\frac{1}{2} (\sqrt{3} - \sqrt{2})$

Solution

$\frac{1}{2} (\sqrt{3 - 1})$

18x2-9πx + π² = 0

(6x -π)(3x-π) = 0

$∴ x = \frac{π}{6}, \frac{π}{3} α = \frac{π}{6}, β = \frac{π}{3} y = (g o f) (x) = \cos x A r e a = \int_{\frac{π}{6}}^{\frac{π}{3}} \cos x d x = (\sin x)_{\frac{π}{6}}^{\frac{π}{3}} = \frac{\sqrt{3}}{2} - \frac{1}{2} = \frac{1}{2} (\sqrt{3} - 1) s q . u n i t s$

Some More Questions From Application of Integrals Chapter

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

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Application Of Integrals

Some More Questions From Application of Integrals Chapter

Solve the following L.P.P. graphically :
Minimise Z = 5x + 10y
Subject to x + 2y ≤ 120
Constraints x + y ≥ 60
x – 2y ≥ 0
and x, y ≥ 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Application Of Integrals

Let g(x) = cos x2, f(x) = x and α, β (α < β) be the roots of the quadrtic equation 18x2 - 9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0 is 12(2-1) 12(3-1) 12(3+1) 12(3-2)

Some More Questions From Application of Integrals Chapter

Solve the following L.P.P. graphically :Minimise Z = 5x + 10ySubject to x + 2y ≤ 120Constraints x + y ≥ 60 x – 2y ≥ 0and x, y ≥ 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve the following L.P.P. graphically :
Minimise Z = 5x + 10y
Subject to x + 2y ≤ 120
Constraints x + y ≥ 60
x – 2y ≥ 0
and x, y ≥ 0