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  • Explain solution rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 47

Explain solution rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 47

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2x^{4}-x^{4}-20\\ hint:\;; Using\;;\int x^{n}dx\\ Given:\;\;If\;\;{f}'(x) =8x^{3}-2x\;\;and\;\;f(2)=8,\;\; find \;\;f(x)\\ Solution:\;\;{f}'(x)=8x^{3}-2x

Integration both side

\begin{aligned} &f(x)=\int\left(8 x^{3}-2 x\right) d x \\ &f(x)=\frac{8 x^{4}}{4}-\frac{2 x^{2}}{2}+c \\ &f(x)=2 x^{4}-x^{2}+c \quad \ldots \ldots(1) \\ &\text { We have } f(2)=8 \\ &\therefore f(2)=2(2)^{4}+(2)^{2}+c=8 \\ &\Rightarrow 32-4+c=8 \Rightarrow c=8-28 \Rightarrow c=-20 \end{aligned}

Put in(1) we get

f(x)=2x^{4}-x^{4}-20\\

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