Zusammenfassung der Ressource
Frage 1
Frage
\( { \rm If} \ u = 2v^{-3} +6v, { \rm \ integrating} \ u \ {\rm with \ respect \ to} \ v\ {\rm gives}\)
Antworten
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\( -v^{-2} +3v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( -0.5v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( -0.5v^{-4} +12v^2\)
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\( -4v^{-2} +12v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( -v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
Frage 2
Frage
\( {\rm Calculate} \ J \ {\rm where} \ J= \int^{0.90}_{0}(17000 +12000x - 28000x^{2})dx \)
Antworten
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\(1.3 \times 10^{4} \)
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\( -1.9\times 10^{3} \)
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\( 4.6\times 10^{3} \)
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\( 2.7\times 10^{4} \)
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\( 1.2\times 10^{4} \)
Frage 3
Frage
\( { \rm If} \ y = 3e^{4x}, { \rm \ integrating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
Antworten
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\( \frac{3}{4}e^{4x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( 12e^{4x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( \frac{3}{4}e^{4x+C}, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( \frac{3}{5}e^{5x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( \frac{3}{4}e^{4x+1} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
Frage 4
Frage
\( { \rm If} \ y = 2{\rm cos}(4x+\pi), { \rm \ integrating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
Antworten
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\( \frac{1}{2}{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( 2{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( -\frac{1}{2}{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( -8{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
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\( \frac{1}{2}{\rm cos}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
Frage 5
Frage
\( { \rm The \ integral \ } \int^{3}_{0}(x(3-x) dx { \rm \ gives \ the \ area \ of \ which \ area \ highlighted \ below?}\)