Answer:
pi
Step-by-step explanation:
First solve the integral
[tex]\int\ {(1+ cos x} )\, dx[/tex]
[tex]\int\ {1} \, dx +\int\ {cos x} \, dx[/tex]
[tex]\int\ {1} \, dx = x[/tex] and [tex]\int\ {cos x} \, dx = sin x[/tex]
x + sin x
Now consider the limit from 0 to π
[tex]\lim_{0 \to \\pi } (x+sin x)[/tex]
(π +sin π) -(0 +sin 0)
sin π = 0 and sin 0 = 0
π-0
π
Answer:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi[/tex]
Remember your antiderivatives!
