The area bounded by the curve y-sin x- y-cos x and y-axis isA- -2B- -2-1C- -2-1D- -2-2

The correct option is C √(2) 1 Area = ∫_0^π/4(cosx sinx)dx = [sin x+cosx ]_0^π/4=1/√(2)+1/√(2) =√(2) 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Parametric Form of a Straight Line

The area boun...

Question

The area bounded by the curve y = sin x, y = cos x and y-axis is

\sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2} + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2} - 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{2} + 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\sqrt{2} - 1$

Area = $\int_{0}^{\frac{π}{4}} (c o s x - s i n x) d x$
$= {[s i n x + c o s x]}_{0}^{\frac{π}{4}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} - = \sqrt{2} - 1$

Suggest Corrections

Similar questions

Choose the correct answer
The area bounded by the Y-axis, y = cos x and y = sin x, $0 \leq x \leq \frac{π}{2}$ is
(a) $2 (\sqrt{2} - 1)$ (b) $\sqrt{2} - 1$
(c) $\sqrt{2} + 1$ (d) $\sqrt{2}$

Q. The area bounded by the y-axis, y = cos x and y = sin x when 0 ≤ x ≤

\frac{π}{2}

is
(a) 2

(\sqrt{2} - 1)

(b)

\sqrt{2} - 1

(c)

\sqrt{2} + 1

(d)

\sqrt{2}

The area bounded by the y-axis, y = cos x and y = sin x when

Q. If the area above the x-axis, bounded by the curves y = 2^kx and x = 0, and x = 2 is

\frac{3}{\log_{e} 2}

, then the value of k is
(a) 1/2
(b) 1
(c) −1
(d) 2

Q. The area bounded by the curve

y = sin x

and

y = cos x

in between

x = 0

and

x = \frac{π}{2}

Join BYJU'S Learning Program

The area bounded by the curve y = sin x, y = cos x and y-axis is

The correct option is C √2−1 Area = ∫π40(cosx−sinx)dx =[sinx+cosx]π40=1√2+1√2−=√2−1

The correct option is C $\sqrt{2} - 1$

Area = $\int_{0}^{\frac{π}{4}} (c o s x - s i n x) d x$
$= {[s i n x + c o s x]}_{0}^{\frac{π}{4}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} - = \sqrt{2} - 1$