Integration

Question 1

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

Accepted Answer

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

Answer

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

Answer

$ -0.5v^{-4} +12v^2$

Answer

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

Answer

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

Question 2

$ {\rm Calculate} \ J \ {\rm where} \ J= \int^{0.90}_{0}(17000 +12000x - 28000x^{2})dx $

Accepted Answer

$1.3 \times 10^{4} $

Answer

$ -1.9\times 10^{3} $

Answer

$ 4.6\times 10^{3} $

Answer

$ 2.7\times 10^{4} $

Answer

$ 1.2\times 10^{4} $

Question 3

$ { \rm If}  \ y = 3e^{4x}, { \rm \ integrating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Question 4

$ { \rm If}  \ y = 2{\rm cos}(4x+\pi), { \rm \ integrating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Question 5

$ { \rm The \ integral \ }  \int^{3}_{0}(x(3-x) dx  { \rm \ gives \ the \ area \ of \ which \ area \ highlighted \ below?}$

Perguntas do quiz (5)