Question

If $\int\limits^a_1 {(3x^{2}+2x+1)} \, dx=11$, find 'a'.

Answer 1

➡️➡️Hope it will help you‼️‼️

Answer 2

Answer:

a = 2

Step-by-step explanation:

$\int\limits^1_a {(3x^2 + 2x + 1)} \, dx = 11$

on integarting

= 3x³/3 + 2x²/2 + x  + c

= x³ + x³ + x + c

on applying limts

1  to 1

= (a³ + a² + a + c) - (1 + 1 + 1 + c)

= a³ + a² + a - 3

a³ + a² + a - 3 = 11

=> a³ + a² + a  - 14 = 0

=> a³ - 2a² + 3a² -6a + 7a  - 14 = 0

=> a²(a - 2) + 3a(a - 2) + 6(a  - 2) = 0

=> (a - 2)(a² + 3a + 6) = 0

=> a = 2    a² + 3a + 6 has imaginary roots