Difference between revisions of "009B Sample Midterm 2, Problem 1"

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(Created page with "<span class="exam">Evaluate the indefinite and definite integrals. ::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}dx</math> ::<span class="exam">b) <math>\int _{\frac{\pi}...")
 
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<span class="exam">Evaluate the indefinite and definite integrals.
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<span class="exam">Consider the region <math>S</math> bounded by <math>x=1,x=5,y=\frac{1}{x^2}</math> and the <math>x</math>-axis.
  
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::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}dx</math>
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::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math>S</math>. Sketch the region <math>S</math> and the rectangles and indicate your rectangles overestimate or underestimate the area of <math>S</math>.
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::<span class="exam">b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}dx</math>
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::<span class="exam">b) Find an expression for the area of the region <math>S</math> as a limit. Do not evaluate the limit.
  
  

Revision as of 17:46, 19 January 2016

Consider the region Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} bounded by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=1,x=5,y=\frac{1}{x^2}} and the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} -axis.

a) Use four rectangles and a Riemann sum to approximate the area of the region Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} . Sketch the region Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} and the rectangles and indicate your rectangles overestimate or underestimate the area of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} .
b) Find an expression for the area of the region Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} as a limit. Do not evaluate the limit.


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