What is f(x) = int (x-3)^2-3x+4 dx if f(2) = 4 ?
2 Answers
Apr 10, 2018
Explanation:
Apr 10, 2018
Explanation:
"expand "(x-3)^2" and simplify"
f(x)=int(x^2-6x+9-3x+4)dx
color(white)(f(x))=int(x^2-9x+13)dx
"integrate each term using the "color(blue)"power rule"
•color(white)(x)int(ax^n)dx=a/(n+1)x^(n+1);n!=-1
rArrf(x)=1/3x^3-9/2x^2+13x+c
"where c is the constant of variation"
"to find c use the condition "(f(2)=4
rArr4=8/3-18+26+crArrc=-20/3
rArrf(x)=1/3x^3-9/2x^2+13x-20/3