# 5: Change the order of integration ∫0∞​∫0x​e−x2

Reversing Order of Integration
Reversing Order of Integration

Question

5: Change the order of integration and evaluate. [B.C. A. (Agra) 2005, 2008; B.C. A. (Lucknow) 2009; B.C. A. (Kanpur We have

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Question 1

5) Evaluate Ans 6) Prove that 7) 8) Show that

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Question 2

TWO MARK QUESTIONS:- 1. Integoate with respect to . $\begin{array}{l} \int \frac{e^{x} x}{(1+x)^{2}} d x \\ =\int e^{x}\left[\frac{1}{x+1}+\frac{-1}{(x+1)^{2}}\right] d x \quad=\frac{x+1}{(x+1)^{2}}-\frac{1}{(x+1)^{2}} \\ =e^{x}\left(\frac{1}{x+1}\right)+c \\ \end{array}$ 2. Evaluate . $\begin{array}{l} \int e^{x} \frac{(x-3)}{(x-1)^{3}} d x \\ \left.=\int e^{x}\left[\frac{1}{(x-1)^{2}}-\frac{2}{(x-1)^{3}}\right] d x\right]=\frac{x-1}{(x-1)^{3}}-\frac{2}{(x-1)^{3}} \\ \text { Let } \left.f(x)=\frac{1}{(x-1)^{2}}, f^{\prime}(x)=\frac{-2}{(x-1)^{3}}\right]=\frac{1}{(x-1)^{2}}-\frac{2}{(x-1)^{3}} \text {. } \\ =e^{x} \frac{1}{(x-1)^{2}}+c . \\ \end{array}$

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Question 3

Let be the region in the first and second quadrants between the graphs of the polar curves and , as shaded in the figure above. Which of the following integral expressions gives the area of ?

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Question 4

24. If , then the value of (a) is 1) (2019 Main, 9 Jan III) (a) 1 (b) 36. The integral (c) 2 (d) 4 (a)

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 Question Text 5: Change the order of integration and evaluate. [B.C. A. (Agra) 2005, 2008; B.C. A. (Lucknow) 2009; B.C. A. (Kanpur We have Updated On Jun 8, 2023 Topic Integration Subject Mathematics Class Class 12 Passed Answer Type Video solution: 1 Upvotes 60 Avg. Video Duration 3 min

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