Question

area bounded by the y axis, y=cosx, y=sinx and 0<x<π/2​​

Answer 1

Explanation:

Finding point of Intersection B

Solving

y=cosx and y=sinx

cosx=sinx

Refer image 2.

At x=

4

π

, both are equal

Also,

y=cosx=cos

4

π

=

2

1

So, B=(

4

π

,

2

1

)

Refer image 3.

Refer image 4.

Area ABCO

Area ABCO ∫

0

π/4

ydx

Here, y=cosx

Thus,

Area ABCO= ∫

0

π/4

cosxdx

=[sinx]

0

π/4

=[sin

4

π

−sin0]

=

2

1

−0

=

2

1

Refer image 5.

Area BCO

Area BCO ∫

0

π/4

ydx

Here, y=sinx

Thus,

Area BCO = ∫

0

π/4

sinxdx

=−[cosx]

0

π/4

=−[cos

4

π

−cos(0)]

=−[

2

1

−1]

=1−

2

1

Therefore

Area Required = Area ABCD - Area BCO

=

2

1

−[1−

2

1

]

=

2

1

+

2

1

−1

=

2

2

−1

=

2

−1