Question

$If \int\limits^1_0 (3x²+2x+K)dx=0, then K=......,Select correct option from the given options.$

(a) 1

(b) 2

(c) -2

(d) 4

Answer 1

HELLO DEAR,

GIVEN:-
$\sf{\int\limits^1_0 (3x^2+2x+K)dx=0}$

so, $\sf{\int\limits^1_0 (3x^2.dx + 2x.dx + k.dx) = 0}$

$\sf{[x^3 + x^2 + kx]^{^1}_0 = 0}$

$\sf{[(1)^3 + (1)^2 + k(1) - (0+0+0) = 0}$

=> 1 + 1 + k = 0

=> k = -2

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Given, $\int\limits^1_0{3x^2+2x+K}\,dx=0$

$\int\limits^1_0{3x^2}\,dx+\int\limits^1_0{2x}\,dx+\int\limits^1_0{K}\,dx=0$

$\left[\begin{array}{c}3\frac{x^3}{3}\end{array}\right]^1_0+\left[\begin{array}{c}2\frac{x^2}{2}\end{array}\right]^1_0+K[x]1_0$

$(1^3-0) + (1^2-0) + K(1 - 0) = 0$

1 + 1 + K = 0

K = -2

hence, option (c) is correct.