What is $f (x) = \int {(3 x + 1)}^{2} - 6 x - 1 d x$ $f(x) = int (3x+1)^2-6x-1 dx$ if $f (2) = 1$ $f(2) = 1$ ?

Question

What is $f (x) = \int {(3 x + 1)}^{2} - 6 x - 1 d x$ $f(x) = int (3x+1)^2-6x-1 dx$ if $f (2) = 1$ $f(2) = 1$ ?

1 Answer

Impact of this question

1430 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-24T13:44:15

$f (x) = 3 x^{3} - 23$ $f(x)=3x^3-23$

Explanation:

The first step is to simplify the expression to be integrated.

${(3 x + 1)}^{2} - 6 x - 1 = 9 x^{2} + 6 x + 1 - 6 x - 1 = 9 x^{2}$ $(3x+1)^2-6x-1=9x^2+6x+1-6x-1=9x^2$

$\Rightarrow \int 9 x^{2} d x$ $rArrint9x^2dx$

integrate using $power rule for integration$ $color(blue)"power rule for integration"$

$color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(intax^n dx=a/(n+1)x^(n+1))color(white)(a/a)|)))$

$rArrint9x^2dx=9/3x^3+c=3x^3+c" c is a constant"$

Using f(2) = 1 allows c to be calculated.

$3(2)^3+c=1rArr24+c=1rArrc=-23$

$rArrf(x)=3x^3-23$

Science

Math

Humanities

... and beyond

What is $f (x) = \int {(3 x + 1)}^{2} - 6 x - 1 d x$ $f(x) = int (3x+1)^2-6x-1 dx$ if $f (2) = 1$ $f(2) = 1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is f(x) = int (3x+1)^2-6x-1 dxf(x)=∫(3x+1)2−6x−1dxf(x) = int (3x+1)^2-6x-1 dx if f(2) = 1 f(2)=1f(2) = 1 ?

1 Answer

Explanation:

Related questions

Impact of this question

What is $f (x) = \int {(3 x + 1)}^{2} - 6 x - 1 d x$ $f(x) = int (3x+1)^2-6x-1 dx$ if $f (2) = 1$ $f(2) = 1$ ?