Integration

Question

\( { \rm If} \ u = 2v^{-3} +6v, { \rm \ integrating} \ u \ {\rm with \ respect \ to} \ v\ {\rm gives}\)

Answer 1

\( -v^{-2} +3v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 2

\( -0.5v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 3

\( -0.5v^{-4} +12v^2\)

Answer 4

\( -4v^{-2} +12v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 5

\( -v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 6

\(1.3 \times 10^{4} \)

Answer 7

\( -1.9\times 10^{3} \)

Answer 8

\( 4.6\times 10^{3} \)

Answer 9

\( 2.7\times 10^{4} \)

Answer 10

\( 1.2\times 10^{4} \)

Answer 11

\( \frac{3}{4}e^{4x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 12

\( 12e^{4x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 13

\( \frac{3}{4}e^{4x+C}, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 14

\( \frac{3}{5}e^{5x} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 15

\( \frac{3}{4}e^{4x+1} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 16

\( \frac{1}{2}{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 17

\( 2{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 18

\( -\frac{1}{2}{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 19

\( -8{\rm sin}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 20

\( \frac{1}{2}{\rm cos}(4x+\pi) +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)

Answer 21

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Answer 22

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Answer 23

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Answer 24

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Answer 25

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Resource summary

	Created by Jackie Grant over 7 years ago