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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 29 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Multiple Choice Questions Question 29 Maths Textbook Solution.

Answers (1)

Answer:

\sin x+C

Given:

\int x \sin x d x=-x \cos x+\alpha

Hint:

You must know the derivation of sin x and rule to integrate by parts.

Explanation:

Let I=\int x \sin x d x

          =x(-\cos x)+\int(1) \cos x d x                              \text { [ : :Integration by parts } \left.\int u . v d x=u \int v d x-\int \frac{d u}{d x} \int v d x d x\right]

          =-x \cos x+\sin x+C

Acc. to given              

\begin{aligned} &I=-x \cos x+\alpha \\ &\Rightarrow-x \cos x+\sin x+C=-x \cos x+\alpha \end{aligned}

Comparing both sides

We get,\alpha=\sin x+C

               

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