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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 18 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 18 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{2} x^{2} \sin x^{2}+\frac{1}{2} \cos x^{2}+c

Hint: Take x^{2}=t

          So we get 2 x d x=d t

                       x d x=\frac{d t}{2}

Given: Let I=\int x^{3} \cos x^{2} d x

Solution: I=\int x^{3} \cos x^{2} d x

We can write it as

             \begin{aligned} &\int x x^{2} \cos x^{2} d x \\ &=\frac{1}{2} \int t \cos t d t=\frac{1}{2}\left(t \int \cos t d t-\int\left[\frac{d t}{d t} \int \cos t d t\right] d t\right) \\ &=\frac{1}{2}\left(t \sin t-\int \sin t d t\right) \end{aligned}

Now by integrating the second part

            =\frac{1}{2}(t \sin t+\cos t)+c

Substituting the value of t as x^{2}

         =\frac{1}{2} x^{2} \sin x^{2}+\frac{1}{2} \cos x^{2}+c

Posted by

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