.1f u and v are functions of x, then Suv dx. = us v dx - scene so dx)dx. Also integrate: x sinx dx
Answers
Answer:
Let u and v be any two functions of x.
Then, by product rule of differentiation
dx
d
(uv)=u
dx
dv
+v
dx
du
Differentiating both sides with respect to x,
uv=∫u
dx
dv
dx+∫v
dx
du
dx
⇒∫u
dx
dv
dx=uv−∫v
dx
du
dx
Now, put u=f
1
(x)
and
dx
dv
=f
2
(x), i.e., v=∫f
2
(x)dx
∫f
1
(x)f
2
(x)dx=f
1
(x)∫f
2
(x)dx−∫[
dx
d
{f
1
(x)}∫f
2
(x)dx]dx
⇒∫u v dx=u∫v dx−∫[
dx
du
∫vdx]dx
Where, u=f
1
(x),v=f
2
(x).
Step-by-step explanation:
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Step-by-step explanation:
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.