the area bounded by the curve y=sinx and y=cosx and y-axis is
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Answer:
ANSWER
Refer image 1.
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