Question

O valor da integral I =
tg’x dx é:
O A) 2+
4
ОВ)
V2
2.
O C) 1-
4
OD)
V21
+
2
O E)
4​

Answer 1

$\displaystyle\mathsf{\int\limits_{0}^{\frac{\pi}{4}}tg^2(x)dx=\int\limits_{0}^{\frac{\pi}{4}}(sec^2(x)-1)dx} \\ \mathsf{=(tg(x)-x)\Bigg|_{0}^{\frac{\pi}{4}}}$

$\mathsf{=(tg(\dfrac{\pi}{4})-\dfrac{\pi}{4}}\\=\large\boxed{\boxed{\boxed{\boxed{\mathsf{1-\dfrac{\pi}{4}}}}}}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\maltese~~alternativa~~c}}}}}$