Linear Algebra
= ∫ [a,b,f(x)g(x) dx]
given:
f(x) =x^2
g(x)= 4-x
[0,4]
find
given:
f(x) =x^2
g(x)= 4-x
[0,4]
find
-
= ∫(x = 0 to 4) x^2 * (4 - x) dx
= ∫(x = 0 to 4) (4x^2 - x^3) dx
= (4x^3/3 - x^4/4) {for x = 0 to 4}
= 64/3.
I hope this helps!
-
Looks like you are finding the norm of a vector the components of which are f(x) and g(x). In this case the norm is defined to be the integral over the closed interval [0,4].
= integral from 0 to 4 of [ (x^2)(4 - x) dx = integral from 0 to 4 [ 4x^2 - x^3 ]dx =
(4/3)x^3 - (1/4)x^4 ] from 0 to 4 = (4/3)64 - (1/4)256 = 256(1/12) = 64/3
I hope you can follow the work; there's no easy way to express the integral sign with this text editor.
(4/3)x^3 - (1/4)x^4 ] from 0 to 4 = (4/3)64 - (1/4)256 = 256(1/12) = 64/3
I hope you can follow the work; there's no easy way to express the integral sign with this text editor.