What is #f(x) = int x^4-x^2+5 dx# if #f(3)=-1 #?

1 Answer
Jim G.
Jun 20, 2016

#1/5x^5-1/3x^3+5x-278/5#

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#

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