## anonymous 5 years ago Estimate the area under the curve cos sqrt x for 0=<x=<2 . Give your answer accurate to 2 significant figures.

1. anonymous

Definite Integrals? Any help..im stuck

2. anonymous

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

3. anonymous

4. anonymous

the problem is we havnt got to trapeziod rule

5. anonymous

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

6. anonymous

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

7. anonymous

Well then you have to estimate with rectangles.

8. anonymous
9. anonymous

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

10. anonymous

It's okay to apply this formula.

11. anonymous

thanks guys

12. anonymous

np