Question

I have a question #14

Answer 1

\[f(x)=x^4+2x^3-x^2+ax+b\]
where
\[f(x)=[Q(x)]^2\]
find \[\int\limits\limits_{0}^{1}f(x)dx=?\]

Answer 2

in fraction form

Answer 3

btw what is Q(x) ?

Answer 4

both f(x) and Q(x) are polynomial functions.- this is what the problem says

Answer 5

ok well i'll translate everything they say in the problem

Answer 6

define:
a and b are real numbers
f(x) is a polynomial function where
\[f(x)=x^4+2x^3-x^2+ax+b\]
if there exist a polynomial function Q(x) where \[f(x)=(Q(x))^2\]
find \[\int\limits_{0}^{1} f(x) dx =?\]

a. \[\frac{71}{30}\]
b. \[\frac{31}{30}\]
c. \[\frac{11}{30}\]
d. \[\frac{1}{30}\]

Hope that there's no mistake in my translation

Answer 7

this is all we get from the problem

Answer 8

11/30

Answer 9

correct ffm plz explain

Answer 10

You don't know how to solve this one ?

Answer 11

or testing me ? :P

Answer 12

both ;P

Answer 13

Okay Let, \( Q(x)= x^2 + P x + Q\) then \( f(x) = Q^2+2 P Q x+P^2 x^2+2 Q x^2+2 P x^3+x^4 \) after this you just need to compare the coefficients and find \( a \) and \( b \) then ...