Question

write the degree of the polynomial x + 9​

Answer 1

Answer:

In order to evaluate this type of Integrals, we may follow the following algorithm.

STEP I    Check whether degree of P(x)≥ or <n.

STEP II    If degree of p(x)<n, express P(x) in the from

                A

0

+A

1

(ax+b)+A

2

(ax+b)

2

+....+A

n−1

(ax+b)

n−1

STEP III    Write 

(ax+b)

2

P(x)

as

(ax+b)

n

A

0

+

(ax+b)

n−1

A

1

+

(ax+b)

n−2

A

2

+....+

ax+b

A

n−1

STEP IV    Evaluate

                ∫

(ax+b)

n

Px

dx=A

0

∫

(ax+b)

n

1

dx+A

1

∫

(ax+b)

n−1

1

dx+....+A

n−1

∫

ax+b

1

dx

STEP V    If degree of P(x)≥n, then divide P(x) by (ax+b)

n

 and express 

(ax+b)

n

P(x)

as Q(x)+

(ax+b)

n

R(x)

, where degree of R(x) is less than n.

STEP VI    Use step II and III to evaluate ∫

(ax+b)

n

R(x)

dx

Medium

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