Question

If f(x) = a + bx + cx², show that $\int\limits^1_0 {f(x)} \, dx= \frac{1}{6}[f(0)+4f(\frac{1}{2})+f(1)]$

Answer 1

➡️Hope it will help you✔️

Answer 2

Answer:

LHS = RHS

Step-by-step explanation:

f(x) = a + bx + cx²

integrating f(x)dx

= ax + bx²/2  + cx³/3 + d

With limit from 0 to 1

= (a + b/2 + c/3 + d) - (0 + 0 + 0 + d)

= a + b/2 + c/3

LHS = a + b/2 + c/3

RHS = (1/6) ( f(0)  + 4f(1/2)  + f(1) )

= (1/6) ( a + 0 + 0 + 4 (a + b/2 + c/4) + a + b + c)

= (1/6) ( a + 4a + 2b + c + a + b + c)

= (1/6)(6a + 3b + 2c)

= a + b/2 + c/3

LHS = RHS