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  • Need solution for RD Sharma Maths Class 12 Chapter 19 Definite Integrals Excercise 19.3 Question 21

Need solution for RD Sharma Maths Class 12 Chapter 19 Definite Integrals Excercise 19.3 Question 21

Answers (1)

Answer:  0

Hint: Use ILATE ,( Inverse , Logarithm , Algebraic , Trigonometric , Exponent.)

Given:

             \int_{-2}^{2} x e^{|x|} d x

Solution:

             Consider

             f(x)=x e^{|x|}

             Now

             \begin{aligned} &f(-x)=(-x) e^{|-x|}=-x e^{|x|}=-f(x) \\ \end{aligned}

             \therefore \int_{-2}^{2} x e^{|x|} d x=0 \\

            {\left[\int_{-a}^{a} f(x) d x=\left\{\begin{array}{ll} 2 \int_{0}^{a} f(x) d x & \text { if } f(-x)=f(x) \\ 0 & \text { if } f(-x)=-f(x) \end{array}\right]\right.}

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