Question

evaluate the intergral \[\int\limits_{0}^{\frac{ \pi }{ 2 }} \sin2xdx\]

Answer 1

you know how to do U-substitution?

Answer 2

yes, is it u=2x?

Answer 3

yes

Answer 4

du=?

Answer 5

du=2dx?

Answer 6

yes

Answer 7

then\[\frac{ 1 }{ 2 }\]du=dx

Answer 8

yes

Answer 9

then so doi integrate the sinu?

Answer 10

yes

Answer 11

integral of 1/2 sin u du from 0 to pi/2

Answer 12

is it cos2x

Answer 13

then plug in the pi/2 and 0?

Answer 14

yes

Answer 15

does the 1/2 multiply with the 2 from the cos2x?

Answer 16

no it doesn't

Answer 17

so it stays a 1/2cos2x

Answer 18

yes

Answer 19

k thank you so much :)