What is #f(x) = int -x^3+3x-4 dx# if #f(2) = -3 #?

1 Answer
Jim G.
Feb 21, 2017

#f(x)=-1/4x^4+3/2x^2-4x+3#

Explanation:

Integrate each term using the #color(blue)"power rule for integration"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(int(ax^n)=a/(n+1)x^(n+1) ; n≠-1)color(white)(2/2)|)))#

#rArrint(-x^3+3x-4)dx#

#f(x)=-1/4x^4+3/2x^2-4x+c#

#"solve for c, given "f(2)=-3#

#-3=-4+6-8+crArrc=3#

#rArrf(x)=-1/4x^4+3/2x^2-4x+3#

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