exercise:Ee40bd229d: Difference between revisions
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Let <math>G(x) = \int_1^x \left( t + \frac1{t^2} \right) \; dt</math>, | Let <math>G(x) = \int_1^x \left( t + \frac1{t^2} \right) \; dt</math>, for <math>x > 0</math>. | ||
for <math>x > 0</math>. | |||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li>Using just the Fundamental Theorem, find <math>G^\prime(x)</math> and <math>G^\prime(2)</math>.</li> | ||
Using just the Fundamental Theorem, | <li>Evaluate <math>G(x)</math> as a rational function of <math>x</math> by finding | ||
find <math>G^\prime(x)</math> and <math>G^\prime(2)</math>.</li> | |||
<li> | |||
Evaluate <math>G(x)</math> as a rational function of <math>x</math> by finding | |||
an antiderivative of <math>t + \frac1{t^2}</math>.</li> | an antiderivative of <math>t + \frac1{t^2}</math>.</li> | ||
<li>Take the derivative of <math>G(x)</math> as found in | <li>Take the derivative of <math>G(x)</math> as found in (b) and thereby check (a).</li> | ||
and thereby check | |||
</ul> | </ul> | ||
Latest revision as of 22:09, 23 November 2024
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[/math]
Let [math]G(x) = \int_1^x \left( t + \frac1{t^2} \right) \; dt[/math], for [math]x \gt 0[/math].
- Using just the Fundamental Theorem, find [math]G^\prime(x)[/math] and [math]G^\prime(2)[/math].
- Evaluate [math]G(x)[/math] as a rational function of [math]x[/math] by finding an antiderivative of [math]t + \frac1{t^2}[/math].
- Take the derivative of [math]G(x)[/math] as found in (b) and thereby check (a).