Difference between revisions of "009B Sample Final 1, Problem 2"
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<span class="exam"> We would like to evaluate | <span class="exam"> We would like to evaluate | ||
| − | + | ::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg).</math> | |
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| − | + | <span class="exam">(a) Compute <math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt.</math> | |
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| − | + | <span class="exam">(b) Find <math style="vertical-align: -5px">f'(x).</math> | |
| − | + | <span class="exam">(c) State the Fundamental Theorem of Calculus. | |
| − | + | <span class="exam">(d) Use the Fundamental Theorem of Calculus to compute <math style="vertical-align: -15px">\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg)</math> without first computing the integral. | |
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| − | + | <hr> | |
| − | + | [[009B Sample Final 1, Problem 2 Solution|'''<u>Solution</u>''']] | |
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| − | + | [[009B Sample Final 1, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']] | |
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[[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] | [[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] | ||
Latest revision as of 17:15, 2 December 2017
We would like to evaluate
- 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 \frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg).}
(a) Compute 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 f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt.}
(b) Find 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 f'(x).}
(c) State the Fundamental Theorem of Calculus.
(d) Use the Fundamental Theorem of Calculus to compute 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 \frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg)} without first computing the integral.