Question

find the exact area under f(x)=x+cosx on [0,pi]

Answer 1

integrate

Answer 2

Answer:Pi^2/2

Answer 3

the cosine function at 0 takes value of 1 and at pi takes -1
so the area under f(x)=cosx from 0 to pi is 0
now you only need to get the f(x)=x from 0 to pi and that is just a triangle

you dont even need integration .-)

Answer 4

yes it is
\[\frac{\pi^2}{2}\]

Answer 5

\[\int_0^{\pi} x + \cos(x)dx\]
\[F(x)=\frac{x^2}{2}-\sin(x)\]
\[F(\pi)-F(0)=\frac{\pi^2}{2}\]

Answer 6

I prefer my solution :-)

Answer 7

yes snappier

Answer 8

Moral: always draw a rough diagram first, to see what's going on