IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

rphy

If P(x) is a polynomial of least degree that has a maximum equal to 6 at x = 1 , and a minimum equal to 2 at x = 3, then ₀

¹ P(x)dx equals
a) 17/4
b)13/4
c)19/4
d)5/4

Please help. Thanks!

nitin62225

ans = 19/4

p(x)=

_{[ ]}

^{[ ]} a(x-1)(x-3)dx

=ax³/3-2ax²+3ax+c

satisfying the given informations, we get

a=3

c=2

so p(x)=x³-6x² +9x +2

integrate and puting limits we get 19/4

plz rate....

rphy

yes. thanks

ank_einstein

it is a 3rd degreee polynomial

let it b f(x)= ax^3 + bx^2 +cx +d.

f'(X)=3ax^2+2bx+c;

f'(1)=0=>3a+2b+c=0;

f'(3)=0=>9a+6b+c=0;

f(1)=a+b+c+d=6;

f(3)=27a+9b+3c+d=2;

solving them we get:

the function f(X);
nitegrating b/w the liomits we get the value .
plz rate me if u find it useful

avinash.sharma

nitin62225 has solven the question perfectly.

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