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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 12 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 12 Maths Textbook Solution.

Answers (1)

Answer:

None of these

Given:

\int|x|^{3} d x

Hint:

Using \int x^{n} d x

Explanation:

Let I=\int|x|^{3} d x

Here two cases arise.

\begin{aligned} &I=\left\{-x^{3}, x<0 ; x^{3}, x \geq 0\right.\\ &\therefore \text { Case I, when } x<0 \end{aligned}

\begin{aligned} &I=\int_{4}-x^{3} d x \\ &=\frac{-x^{4}}{4}+C \end{aligned}                                                            \left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+C\right]

\text { Case II, when } x \geq 0

\begin{aligned} &I=\int_{4} x^{3} d x \\ &=\frac{x^{4}}{4}+C \end{aligned}                                                                    \left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+C\right]

Combining these two, we get

I=\pm \frac{x^{4}}{4}+C

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