integration?

Question

integrate e^tanx/cos²x dx from [0, π/4]

a) 0
b) 1
c) e-1
d) e
f) e+1

Answer 1

observe that d/dx(tanx) = 1/cos²x

so integral of e^tanx/cos²x is e^tanx
so if you integrate from [0, ], you will get e^tan(π/4) - e^tan(0), which is e - 1

hence, the answer is c

Answer 2

The answer is "c".
_______
Reason:
∫e^tanx/cos²x dx from [0, π/4]
= ∫e^tanx d(tanx) from [0, π/4], mental substitution
= e^tanx from [0, π/4]
= e-1

Answer 3

If you put tanx =z 1/cos^2x dx = dz and you have the integral from

0 to 1 of e^z dz which is e-1 (c)

Answer 4

c

Answer 5

c