157k views
8 votes
Evaluate the integral, please help!!!


\int_(0)^(\pi)(1+cosx) dx

User TableCreek
by
3.5k points

2 Answers

1 vote

Answer:


\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi

Explanation:


\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^(\pi)_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi

Remember your antiderivatives!

User Boude
by
3.4k points
4 votes

Answer:

pi

Explanation:

First solve the integral


\int\ {(1+ cos x} )\, dx


\int\ {1} \, dx +\int\ {cos x} \, dx


\int\ {1} \, dx = x and
\int\ {cos x} \, dx = sin x

x + sin x

Now consider the limit from 0 to π


\lim_(0 \to \\pi ) (x+sin x)

(π +sin π) -(0 +sin 0)

sin π = 0 and sin 0 = 0

π-0

π

User Cannon
by
3.5k points