Question

Find area
of region
bounded by the curves
y1 = sinx & y2 = cosx between x= 0 and x= π/4​

Answer 1

Answer:

this related question

Step-by-step explanation:

Explanation:

The Area due to

x-axis

between two curves given by:

A

=

∫

b

a

y

2

−

y

1

⋅

d

x

The interval of our integral

x

∈

[

π

4

,

5

π

4

]

now let set up the integral:

A

=

∫

5

π

4

π

4

sin

x

−

cos

x

⋅

d

x

=

[

−

cos

x

−

sin

x

]

5

π

4

π

4

[

(

−

sin

(

5

π

4

)

−

cos

(

5

π

4

)

)

−

(

−

sin

(

π

4

)

−

cos

(

π

4

)

)

]

[

2

√

2

+

2

√

2

]

=

4

√

2

=

2

√

2

show the wanted area below(shaded):

y

=

sin

x

blue curve

y

=

cos

x

green curve