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

1 Answer
Oct 8, 2016

#y=-1/3x^3+1/2x^2-4x+17/3#

Explanation:

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

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

#rArrint(-x^2+x-4)dx#

#y=-1/3x^3+1/2x^2-4x+c#

To find c, the constant of integration, substitute x = 2 , y = - 3

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

#rArrc=-3+8/3-2+8=5 2/3=17/3#

#rArry=-1/3x^3+1/2x^2-4x+17/3#