Question

If g(x) = (ax² + bx + c)sinx + (dx² + e^x + f ) cos x then find the values of a, b, c, d, e and f such that g'(x) = x²sinx.

Answer 1

Given g(x) = (ax² + bx + c)sinx + (dx² + ex + f) cos x

⇒ g'(x) = (2ax + b)sinx + (ax² + bx + c)cos x + (2dx + e)cos x – (dx² + e^x + f)sinx

= (2ax + b – dx² – e^x – f)sinx + (2 + bx + c + 2 + e)cos x

Comparing the co-efficients of sin x and cos x, we

get, (2ax + b – dx² – e^x – f) = x²

and (ax² + bx + c + 2dx + e) = 0