Question

calcule a integral de
cos^2 (x) dx com intervalo de pi/2 até -pi/2​

Answer 1

Resposta:

π/2

Explicação passo-a-passo:

∫cos²(x) dx =

∫[1+cos(2x)]/2 dx

∫[1/2+[cos(2x)]/2 dx =

∫[1/2dx+∫[cos(2x)]/2 dx =

x/2 + (1/2)∫cos(2x)dx =

x/2 + (1/2)(1/2)sen2x

[x/2 + (1/4)sen2x] de -π/2 a 0

0-[(-π/4) + (1/4).0]= π/4

[x/2 + (1/4)sen2x] de 0 a π/2

π/4 + (1/4).0 -[(0)] = π/4

π/4 + π/4= π/2