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

1 Answer
Jim G.
Aug 24, 2016

#f(x)=3x^3-23#

Explanation:

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

#(3x+1)^2-6x-1=9x^2+6x+1-6x-1=9x^2#

#rArrint9x^2dx#

integrate using #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#

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