Let px be a function defined on R such that p-x-p-1-x- for all x -0-1- p0-1 and p1-41- Then -01 px d x equalsA- 21B- 41C- 42D- -41

The correct option is A 21p'(x)=p'(1 x) ⇒ p(x)= p(1 x)+c Put x=0 p(0)= p(1)+c ⇒ c = 42 I=∫_0^1 p(x)dx I =∫_0^1p(1 x)dx 2I=∫_0^1(p(x)+p(1 x))dx=∫_0^1 c dx=∫_0^1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

Let px be a f...

Question

Let p(x) be a function defined on R such that p’(x) = p’(1–x), for all x $ϵ$ [0, 1], p(0) = 1 and p(1) = 41. Then $\int_{0}^{1} p (x) d x$ equals

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{41}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 21
$p^{'} (x) = p^{'} (1 - x)$
$\Rightarrow p (x) = - p (1 - x) + c$
$P u t x = 0$
$p (0) = - p (1) + c$
$\Rightarrow c = 42$
$I = \int_{0}^{1} p (x) d x$
$I = \int_{0}^{1} p (1 - x) d x$
$2 I = \int_{0}^{1} (p (x) + p (1 - x)) d x = \int_{0}^{1} c d x = \int_{0}^{1} 42 d x$
$2 I = 42 \Rightarrow I = 21$

Suggest Corrections

Similar questions

Q. Let

p (x)

be a function defined on

R

such that

p^{'} (x) = p^{'} (1 - x)

, for all

x ϵ [0, 1], p (0) = 1

and

p (1) = 41

. Then

\int_{0}^{1} p (x) d x

equals

Q. Let

p (x)

be a function defined on

R

such that

p^{'} (x) = p^{'} (1 - x)

, for all

x \in [0, 1], p (0) = 1

and

p (1) = 41

. Then

\int_{0}^{1} p (x)

dx equals

Q. Let p(x) be a function defined on R such that p’(x) = p’(1–x), for all x

ϵ

[0, 1], p(0) = 1 and p(1) = 41. Then

\int_{0}^{1} p (x) d x

equals

Q. Let

P

be a non-zero polynomial such that

P (1 + x) = P (1 - x)

for all real

x

, and

P (1) = 0

. Let

m

be the largest integer such that

(x - 1)^{m}

divides

P (x)

for all such

P (x)

. Then

m

equals

Q. If

P (x)

is a polynomial of degree less than or equal to

2

and

S

is the set of all such polynomials so that

P (1) = 1, P (0) = 0

and

P^{'} (x) > 0

\forall

x \in [0, 1]

, then

Join BYJU'S Learning Program

Let p(x) be a function defined on R such that p’(x) = p’(1–x), for all x ϵ [0, 1], p(0) = 1 and p(1) = 41. Then ∫10p(x)dx equals

The correct option is A 21p′(x)=p′(1−x) ⇒p(x)=−p(1−x)+c Put x=0 p(0)=−p(1)+c ⇒c=42 I=∫10p(x)dx I=∫10p(1−x)dx 2I=∫10(p(x)+p(1−x))dx=∫10 c dx=∫1042 dx 2I=42 ⇒I=21

Let p(x) be a function defined on R such that p’(x) = p’(1–x), for all x $ϵ$ [0, 1], p(0) = 1 and p(1) = 41. Then $\int_{0}^{1} p (x) d x$ equals