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Byju's Answer
Standard XII
Mathematics
Area between Two Curves
Sketch the gr...
Question
Sketch the graph y = | x + 3 |. Evaluate
∫
-
6
0
x
+
3
d
x
. What does this integral represent on the graph?
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Solution
We have,
y = | x + 3 | intersect x = 0 and x = −6 at (0, 3) and (−6, 3)
Now,
y
=
x
+
3
=
x
+
3
For
all
x
>
-
3
-
x
+
3
For
all
x
<
-
3
Integral represents the area enclosed between x =
−
6
and x = 0
∴
A
=
∫
-
6
0
y
d
x
=
∫
-
6
-
3
y
d
x
+
∫
-
3
0
y
d
x
=
∫
-
6
-
3
-
x
+
3
d
x
+
∫
-
3
0
x
+
3
d
x
=
-
x
2
2
+
3
x
-
6
-
3
+
x
2
2
+
3
x
-
3
0
=
-
9
2
-
9
-
36
2
+
18
+
0
+
0
-
9
2
+
9
=
-
9
2
+
9
+
36
2
-
18
-
9
2
+
9
=
9
sq
.
units
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Similar questions
Q.
Sketch the graph y = | x + 3 |. Evaluate
∫
-
6
0
x
+
3
d
x
. What does this integral represent on the graph?