Estimate the area under the curve cos sqrt x for 0=

Question

Estimate the area under the curve cos sqrt x  for  0=<x=<2 . Give your answer accurate to 2 significant figures.

anonymous · Answer

Definite Integrals? Any help..im stuck

anonymous · Answer

Use trapezoidal rule.  If you look at a plot of your function, you'll see that it falls roughly linearly from 0 to 2.

anonymous · Answer

The answer with trap. rule would be about 1.156

anonymous · Answer

the problem is we havnt got to trapeziod rule

anonymous · Answer

Not sure why it's asking you to estimate when you can solve it exactly with a u sub then by parts.

anonymous · Answer

$$\int\limits_{a}^{b} f(x)dx  \approx (b-a)\frac{f(a)+f(b)}{2}$$

anonymous · Answer

Well then you have to estimate with rectangles.

anonymous · Answer

http://www.wolframalpha.com/input/?i=integral+cos%28sqrt%28x%29%29+from+x%3D0..2

anonymous · Answer

You should know that the area of a trapezoid is $$\frac{1}{2}(a+b)h$$where a and b are the 'top' and 'bottom' and h is the altitude (or height).

Here, a=f(0), b=f(2) and the height is (b-a)=2

anonymous · Answer

It's okay to apply this formula.

anonymous · Answer

thanks guys

anonymous · Answer

np