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The area bounded by the curve y=sinx and y=cosx and y-axis is |
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Answer» 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 |
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