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Use the trigonometric and substitution techniques to evaluate the following integration problems. Complete the following statements by choosing the correct answer for u(x)u(x)  and dudu that you use to solve the problem and the final result for each integration. Please note that we write x^2 to mean x2x2.   1.  ∫0π/23cos3x sin2x  dx=∫0π/23cos3⁡x sin2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=  .   2. ∫0π/4tan3xsec2x  dx=∫0π/4tan3⁡xsec2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=

Use the trigonometric and substitution techniques to evaluate the following integration problems. Complete the following statements by choosing the correct answer for u(x)u(x)  and dudu that you use to solve the problem and the final result for each integration. Please note that we write x^2 to mean x2x2.   1.  ∫0π/23cos3x sin2x  dx=∫0π/23cos3⁡x sin2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=  .   2. ∫0π/4tan3xsec2x  dx=∫0π/4tan3⁡xsec2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the trigonometric and substitution techniques to evaluate the following integration problems. Complete the following statements by choosing the correct answer for u(x)u(x)  and dudu that you use to solve the problem and the final result for each integration. Please note that we write x^2 to mean x2x2.

 

1.  ∫0π/23cos3x sin2x  dx=∫0π/23cos3⁡x sin2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=  .

 

2. ∫0π/4tan3xsec2x  dx=∫0π/4tan3⁡xsec2⁡x  dx=   , when we set u(x)=u(x)=  and du=du=  .

 

3.  ∫2/π∞sin(1/x)x2  dx=∫2/π∞sin⁡(1/x)x2  dx=  , we need to set u(x)=u(x)=  and du=du=  .

 

4.  ∫2∞2(x−1)2  dx=∫2∞2(x−1)2  dx=  , we need to set u(x)=u(x)=  and du=du=  .

 

5.  ∫1∞2(x−1)2  dx=

 

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