What is #f(x) = int -x+4 dx# if #f(1)=-2 #?
1 Answer
Sep 7, 2016
Explanation:
Integrate each term using
#color(blue)"power rule for integration"#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(int(ax^n)dx=a/(n+1)x^(n+1))color(white)(a/a)|)))#
#rArrint(-x+4)dx=-1/2x^(1+1)+4x^(0+1)+c#
#rArrF(x)=-1/2x^2+4x+c# where c is the constant of integration.
We can find the value of c, using f(1) = -2. Substitute in F(x)
That is
#(-1/2xx1^2)+(4xx1)+c=-2#
#rArr-1/2+4+c=-2rArrc=-2-4+1/2=-11/2# Thus
#F(x)=-1/2x^2+4x-11/2#
