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Question

Question: \(\int _ { \pi / 2 } ^ { 3 \pi / 2 } [ 2 \cos \mathrm { x } ]\) dx ([.] ® G. I. F) =...

∫π/23π/2[2cos⁡x]\int _ { \pi / 2 } ^ { 3 \pi / 2 } [ 2 \cos \mathrm { x } ] dx ([.] ® G. I. F) =

A

5π3\frac { 5 \pi } { 3 }

B

−5π3- \frac { 5 \pi } { 3 }

C

–p

D

–2p

Answer

−5π3- \frac { 5 \pi } { 3 }

Explanation

Solution

∫π/23π/2[2cos⁡x]dx\int _ { \pi / 2 } ^ { 3 \pi / 2 } [ 2 \cos x ] d x =

+ + ∫4π33π/2(−1)dx\int _ { \frac { 4 \pi } { 3 } } ^ { 3 \pi / 2 } ( - 1 ) \mathrm { dx } = −5π3\frac { - 5 \pi } { 3 }