Question

definite integral from -pi/2 to 0 (2+tan1/2)sec^2 t/2 dt

Answer 1

there tan1/2 t right ?

Answer 2

sorry, it is actually tan t/2

Answer 3

ok, use by integral substitution
u = tan 1/2 t
du = .... ?

Answer 4

opss.. u = 2+tan1/2 t, i meant :)

Answer 5

where did you take the half from?

Answer 6

u = 2 + tan1/2 t
du = 0 + 1/2 sec^2 1/2 t dt right ?

Answer 7

definite integral from -pi/2 to 0 (2+tan t/2)sec^2 t/2 dt

Answer 8

When deciding what to make your substitution with, you should consider what in the integral has its derivative in there too. This sort of is the process of reversing the chain rule. In this case you should remember that the derivative of tangent is secant squared.

Answer 9

agreed ^

Answer 10

so where did u get that 1/2 from? I did not get it, sorry

Answer 11

\[\frac{ t }{ 2 }=\frac{ 1 }{ 2 }t\]

Answer 12

In the same way 4/2 is equal to 4*(1/2)

Answer 13

oh okay,

Answer 14

by using the chain rule :
if y=tanAx then y'=A*sec^2 Ax

Answer 15

with A is a constant

Answer 16

okay

Answer 17

so, the integration will be
int 2u du right ?

Answer 18

ye

Answer 19

ok, what's the result it ...?

Answer 20

int 2u du = ... ?

Answer 21

sec^2 i/2 t^2/2

Answer 22

int (2u du) = u^2 right ?

Answer 23

I am confused,

Answer 24

i got it,