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Exercise 8: Compute x/1 – x4 dx via: (a) Using a trigonometric substitution x2 (b) Using a hyperbolic substitution x2 (c) Using a u-substitution u = x², and then proceeding in a more normal fashion. Remark: In parts (a) and (c), you should get an expression involving arcsin (hopefully the same one), but in part (b) you should get an expression involving arctan. Since these are both integrals of an everywhere continuous (where defined) function, they are apparently different up to a constant. Try to show this explicitly. = sin 0. tanh 0.

Exercise 8: Compute x/1 – x4 dx via: (a) Using a trigonometric substitution x2 (b) Using a hyperbolic substitution x2 (c) Using a u-substitution u = x², and then proceeding in a more normal fashion. Remark: In parts (a) and (c), you should get an expression involving arcsin (hopefully the same one), but in part (b) you should get an expression involving arctan. Since these are both integrals of an everywhere continuous (where defined) function, they are apparently different up to a constant. Try to show this explicitly. = sin 0. tanh 0.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 30EQ
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Exercise 8: Compute x/1 – x4 dx via: (a) Using a trigonometric substitution x2 (b) Using a hyperbolic substitution x2 (c) Using a u-substitution u = x², and then proceeding in a more normal fashion. Remark: In parts (a) and (c), you should get an expression involving arcsin (hopefully the same one), but in part (b) you should get an expression involving arctan. Since these are both integrals of an everywhere continuous (where defined) function, they are apparently different up to a constant. Try to show this explicitly. = sin 0. tanh 0.
Transcribed Image Text:Exercise 8: Compute x/1 – x4 dx via: (a) Using a trigonometric substitution x2 (b) Using a hyperbolic substitution x2 (c) Using a u-substitution u = x², and then proceeding in a more normal fashion. Remark: In parts (a) and (c), you should get an expression involving arcsin (hopefully the same one), but in part (b) you should get an expression involving arctan. Since these are both integrals of an everywhere continuous (where defined) function, they are apparently different up to a constant. Try to show this explicitly. = sin 0. tanh 0.
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