What is #f(x) = int x^4-x^2+5 dx# if #f(3)=-1 #?
1 Answer
Jun 20, 2016
Explanation:
To integrate use the
#color(blue)"power rule"#
#int(ax^n)dx=(ax^(n+1))/(n+1)# This rule can be applied to each term in the integral.
#int(x^4-x^2+5)dx=1/5x^5-1/3x^3+5x+c# where c is the constant of integration
To find c use f(3) = -1
#rArr1/5(3)^5-1/3(3)^3+5(3)+c=-1#
#rArr243/5-9+15+c=-1rArrc=-278/5#
#rArrF(x)=1/5x^5-1/3x^3+5x-278/5#
