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Please Solve R.D.Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1  Question 1 Maths textbook Solution.

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Answer: 2

Hint:Use indefinite formula to solve the integral and then put the value of limit to get the required answer.

Given: \int_{4}^{9}\frac{1}{\sqrt{x}}dx


\begin{aligned} &\int_{4}^{9} \frac{1}{\sqrt{x}} d x=\int_{4}^{9} x^{-\frac{1}{2}} d x=\left[\frac{x^{\frac{1}{2}+1}}{-\frac{1}{2}+1}\right]_{4}^{9} \quad\left[\int x^{n+1} d x=\frac{x^{n+1}}{n+1}\right] \\ &=\left[\frac{x^{\frac{1}{2}}}{\frac{1}{2}}\right]_{4}^{9} \\ &=2\left[x^{\frac{1}{2}}\right]_{4}^{9} \\ &=2\left[9^{\frac{1}{2}}-4^{\frac{1}{2}}\right] \\ &=2\left[3^{2 \times \frac{1}{2}}-2^{2 \times \frac{1}{2}}\right] \\ &=2[3-2]=2 \end{aligned}

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