exercise:4160af81f0: Difference between revisions
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Let <math>n</math> be a positive integer. | Let <math>n</math> be a positive integer. | ||
<ul style{{=}}"list-style-type:lower-alpha"><li>Evaluate <math>\int_a^b x^n \; dx</math>.</li> | <ul style{{=}}"list-style-type:lower-alpha"><li>Evaluate <math>\int_a^b x^n \; dx</math>.</li> | ||
<li> | <li>Evaluate <math>\int_a^b \frac1{x^n} \; dx</math> provided (i) <math>n \ne 1</math>, and (ii) <math>a</math> and <math>b</math> are either | ||
Evaluate <math>\int_a^b \frac1{x^n} \; dx</math> provided | |||
(i) <math>n \ne 1</math>, and (ii) <math>a</math> and <math>b</math> are either | |||
both positive or both negative.</li> | both positive or both negative.</li> | ||
<li>In | <li>In (b), what is the reason for proviso (i)? For provision (ii)?</li> | ||
For | |||
</ul> | </ul> | ||
Latest revision as of 22:08, 23 November 2024
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[/math]
Let [math]n[/math] be a positive integer.
- Evaluate [math]\int_a^b x^n \; dx[/math].
- Evaluate [math]\int_a^b \frac1{x^n} \; dx[/math] provided (i) [math]n \ne 1[/math], and (ii) [math]a[/math] and [math]b[/math] are either both positive or both negative.
- In (b), what is the reason for proviso (i)? For provision (ii)?