Let f(x)= 2x^ 3 -1 x^ 2

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Let f(x)=2x3−1x2,x≠0.f(x)=\frac{2x^{3}-1}{x^{2}},\quad x\neq 0. Solve the following. (i) Simplify f(x)f(x) into a sum of elementary power functions. (ii) Find the most general function FF such that F′(x)=f(x)F'(x)=f(x). (iii) Show that if F1F_{1} and F2F_{2} are any two functions satisfying F1′(x)=F2′(x)=f(x)F'_{1}(x)=F'_{2}(x)=f(x), then F1(x)−F2(x)F_{1}(x)-F_{2}(x) is a constant.

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