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Byju's Answer
Standard XII
Mathematics
Property 7
Area bounded ...
Question
Area bounded by the curve y = sin x between x = 0 and x = 2
π
is
A
2 sq. unit
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B
4 sq. unit
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C
8
sq. unit
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D
None of these
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Solution
The correct option is
B
4 sq. unit
We have y = sin x
x
0
π
6
π
2
π
3
π
2
2
π
y
0
0.5
1
0
−
1
0
Join these points with a free hand to obtain a rough sketch
Required area = (area of OAB) + (area of BCD)
=
∫
π
0
y
d
x
+
∫
2
π
π
(
−
y
)
d
x
,
(
∵
Area BCD is below x - axis)
=
∫
π
0
s
i
n
x
d
x
−
∫
2
π
π
s
i
n
x
d
x
=
4
s
q
.
u
n
i
t
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Similar questions
Q.
The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq. units