Let polynomials Pn(x) n=0,1,2,3 ...... , be defined by P0(x)=1
P_{n}(x) = \frac{1}{n!}\frac{d^{n}}{dx^{n}}[x^{n}(1-x)^{n}] , n\geq 1
Answer the following Q's
1)
The \int_{0}^{1}{P_{n}(x)}x^{k}dx , 0\leq k<n is equla to
a) (n-1)/(k+1)
b) k/(1+n)
c) 0
d) k/ (n+1)(k+1)
2)Let Q(x) be a polynomial of degree n , for which \int_{0}^{1}{Q(x)x^{m}}dx=0
holds for all integers 0\leq m<n
Let c be a constant such that Q(x) -c Pn(x) is of degree (n-1)
then the integral \int_{0}^{1}{(Q(x)-cP_{n}(x))^{2}}dx
is equal to
A) (1+c2)/(n+1)
B) c2/(n+1)
C)0
D)(Pn-1)2
3)Let Q(x) be a polynomail of degree 10 such that \int_{0}^{1}{Q(x)x^{k}}dx = 0 for all integers 0\leq k<9
If Q(0) = 1 , then integral \int_{0}^{1}{(Q(x))^{2}}dx
is equal to
A) 1/21
B)3/21
C)2/7
D)3/7
1the first one is right . second is wrong .
and method post karo .
did u arrive at it using this ?
\int_{a}^{b}{f(x)}dx = \int_{a}^{b}{f(a+b-x)}dx
only asking baad me kya karna hai ??? mughe thoda problem ho rahahai soln post karo na poora if possible
21DA CAN U INSERT brackets in defining Pn(x) pata nahi chal raha wat is inside the nth derivative and wats inside..
