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  • Please Solve R.D. Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1 Question 8 Maths textbook Solution.

Please Solve R.D. Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1 Question 8 Maths textbook Solution.

Answers (1)

Answer:1

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

Given: \int_{0}^{\infty }e^{-x}dx

Solution:

\int_{0}^{\infty }e^{-x}dx=\left [ \frac{e^{-x}}{-1} \right ]^{\infty }_{0}                                                                    \left ( \int e^{ax}=dx\frac{e^{ax}}{a} \right )

\begin{aligned} &=-1\left[e^{-x}\right]_{0}^{\infty} \\ &=-\left[e^{-\infty}-e^{-0}\right]=-\left[e^{-\infty}-e^{0}\right] \\ &=-1[0-1]=-1(-1) \\ &=1 \end{aligned} \quad\left[e^{-\infty}=0, e^{0}=1\right]

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