evaluate y cosy integration with respect to y
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Calculus Examples
Popular Problems Calculus Evaluate integral of ysin(y) with respect to y
∫
y
sin
(
y
)
d
y
Integrate by parts using the formula
∫
u
d
v
=
u
v
−
∫
v
d
u
, where
u
=
y
and
d
v
=
sin
(
y
)
.
y
(
−
cos
(
y
)
)
−
∫
−
cos
(
y
)
d
y
Simplify.
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−
y
cos
(
y
)
−
∫
−
cos
(
y
)
d
y
Since
−
1
is constant with respect to
y
, move
−
1
out of the integral.
−
y
cos
(
y
)
−
−
∫
cos
(
y
)
d
y
Simplify.
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−
y
cos
(
y
)
+
∫
cos
(
y
)
d
y
The integral of
cos
(
y
)
with respect to
y
is
sin
(
y
)
.
−
y
cos
(
y
)
+
sin
(
y
)
+
C
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