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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 19 definite Integrals Exercise 19.1 Question 32 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 19 definite Integrals Exercise 19.1 Question 32 Maths Textbook Solution.

Answers (1)

Answer:

        2log2-1

Hint: Use indefinite integral formula and then put the limits to solve this integral

Given:

             \int_{1}^{2}log\; xdx

Solution:

              \int_{1}^{2}log\; xdx

Integrating by parts, then

\begin{aligned} &\int_{1}^{2} \log x d x=\left[\log x \int 1 d x\right]_{1}^{2}-\int_{1}^{2}\left[\frac{d}{d x}(\log x) \int 1 d x\right] d x \\ &=[\log x x]_{1}^{2}-\int_{1}^{2} \frac{1}{x} x d x \quad\left[\because \int 1 d x=x ; \frac{d}{d x}(\log x)=\frac{1}{x}\right] \\ &=[2 \log 2-11 \log 1]-\int_{1}^{2} 1 d x \quad\left[\because \int 1 d x=x, \log 1=0\right] \end{aligned}

\begin{aligned} &=[2 \log 2-1(0)]-[x]_{1}^{2} \\ &=2 \log 2-[2-1] \\ &=2 \log 2-1 \end{aligned}

 

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