find a

Question

+2

648

1

$\int_1^a(3x^2-6x+3)dx=27$

Guest Jun 6, 2018

+985

+1

Best Answer

$\text{Find } a: \int_1^a(3x^2-6x+3)dx=27$

After factoring the integrand:	$\int_1^a3(x-1)^2dx=(x-1)^3\|_1^a=(a-1)^3=27$
Taking the cube root:	$a-1=3 \Rightarrow a=\boxed4$

$\text{The solution you seek is } a=\boxed4\\$

GYanggg Jun 6, 2018

GYanggg · Answer 1 · 2018-06-06T07:49:16

$\text{Find } a: \int_1^a(3x^2-6x+3)dx=27$

After factoring the integrand:	$\int_1^a3(x-1)^2dx=(x-1)^3\|_1^a=(a-1)^3=27$
Taking the cube root:	$a-1=3 \Rightarrow a=\boxed4$

$\text{The solution you seek is } a=\boxed4\\$

​ find a