Area bounded by f(x)= max.( sin x, cos x) ∀ 0 ≤ x ≤ (π/2) and the co-ordinate axis is equal to

Question

Area bounded by f(x)= max.( sin x, cos x) ∀ 0 ≤ x ≤ (π/2) and the co-ordinate axis is equal to (A) (1/√2) sq.units (B) √2 sq.units (C) 2 sq.units (D) 1 sq.units

Tardigrade Admin · Accepted Answer

f(x)= cos x ∀ 0 ≤ x ≤ (π/4) = sin x ∀ (π/4) < x < (π/2) ∴ Required area = ∫ limits0π /4 cos xdx

Q. Area bounded by $f (x) = ma x . (sin x, cos x) \forall 0 \leq x \leq \frac{π}{2}$ and the co-ordinate axis is equal to

$\frac{1}{2}$ sq.units

$2$ sq.units

$2$ sq.units

1 sq.units

$f (x) = cos x \forall 0 \leq x \leq \frac{π}{4}$
$= sin x \forall \frac{π}{4} < x < \frac{π}{2}$
$∴$ Required area = $0 \int π /4 cos x d x$

Q. Area bounded by f(x)=max.(sinx,cosx)∀0≤x≤2π​ and the co-ordinate axis is equal to

2​1​ sq.units

2​ sq.units

2 sq.units

1 sq.units

f(x)=cosx∀0≤x≤4π​ =sinx∀4π​<x<2π​ ∴ Required area = 0∫π/4​cosxdx

Q. Area bounded by $f (x) = ma x . (sin x, cos x) \forall 0 \leq x \leq \frac{π}{2}$ and the co-ordinate axis is equal to

$\frac{1}{2}$ sq.units

$2$ sq.units

$2$ sq.units

$f (x) = cos x \forall 0 \leq x \leq \frac{π}{4}$
$= sin x \forall \frac{π}{4} < x < \frac{π}{2}$
$∴$ Required area = $0 \int π /4 cos x d x$