find the derivative and integrations of following function with respect to S
1) x square + sinx
Answers
Answered by
0
Answer:
Mark my answer brainliest
Explanation:
ANSWER
Let f(x)=sin(x
2
+5)
Thus using chain rule,
f
′
(x)=
dx
d
(sin(x
2
+5))⋅
dx
d
(x
2
+5)
=cos(x
2
+5)⋅2x=2xcos(x
2
Answered by
0
Answer:
Use integration by parts, twice.
Let
u
=
x
2
and
d
v
=
sin
x
d
x
. Then
d
u
=
2
x
d
x
and
v
=
−
cos
x
.
∫
(
u
d
v
)
=
u
v
−
∫
(
v
d
u
)
∫
(
x
2
sin
x
)
=
−
x
2
cos
x
−
∫
(
−
cos
x
⋅
2
x
d
x
)
∫
(
x
2
sin
x
)
=
−
x
2
cos
x
+
2
∫
(
x
cos
x
d
x
)
Now, let
u
=
x
and
d
v
=
cos
x
d
x
. Then
d
u
=
d
x
and
v
=
sin
x
. Now, use integration by parts again.
∫
(
x
2
sin
x
)
=
−
x
2
cos
x
+
2
(
x
sin
x
−
∫
(
sin
x
)
)
+
C
∫
(
x
2
sin
x
)
=
−
x
2
cos
x
+
2
x
sin
x
+
2
cos
x
+
C
∫
(
x
2
sin
x
)
=
(
2
−
x
2
)
cos
x
+
2
x
sin
x
+
C
Hopefully this helps!
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