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

2 Answers

7/3

Explanation:

int(x-3)^2-3x+4 dx
= (x-3)^3/3-(3x^2)/2+4x+C
= (2-3)^3/3-(3(2)^2)/2+4(2)+C = 4
= -1/3-6+8+C = 4
= 5/3+C = 4
C = 7/3

Apr 10, 2018

f(x)=1/3x^3-9/2x^2+13x-20/3

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