# calculus

posted by .

consider the integral [cos(x^3)dx,0,0.5]. Approximating it by the Midpoint Rule with n equal subintervals, give an estimate for n which guarantees that the error is bounded by 1/10^4

• calculus -

I get n=8
with integral value = 0.4995

wolframalpha says its actually 0.499442

## Similar Questions

1. ### Integration

What is integral [0 to 2] e^-x^2 dx You are talking about the error function. That integral cannot be expressed in a closed form in terms of other simple functions. The answer I get, taken from an error function table, is 0.99532 * …
2. ### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... …
3. ### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... …
4. ### Calculus - Derivatives

The approximation to a definite integral using n=10 is 2.346; the exact value is 4.0. If the approximation was found using each of the following rules, use the same rule to estimate the integral with n=30. A) Left Rule B) Trapezoid …
5. ### math

(a) Use the Midpoint Rule and the given data to estimate the value of the integral I. (Give the answer to two decimal places.) I = int_0^3.2 f(x)dx 1 x f(x) x f(x) 0.0 7.3 2.0 8.8 0.4 6.8 2.4 7.3 0.8 8.1 2.8 7.6 1.2 7.6 3.2 7.3 1.6 …
6. ### calculus

How large does N have to be in order to approximate the integral of cos(x^2) from 0 to 1, using the Midpoint Rule, with error at most 10^(-6)?
7. ### Math: Calculus

Estimate the area under the graph of f(x)=3x^3+5 from x=-1 to x=4, first using 5 approximating rectangles and right endpoints, and then improving your estimate using 10 approximating rectangles and right endpoints. I'm having problem …
8. ### Calculus

Assume that a>0. Evaluate the integral from 0 to a of x dx by approximating the region bounded by y=x and the x-axis from 0 to a with rectangles. Use equal subintervals and take right endpoints.
9. ### Calculus

a) Estimate the area under the graph of f(x)=7+4x^2 from x=-1 to x=2 using three rectangles and right endpoints. R3= ?
10. ### Calculus

Use the midpoint rule with n=4 to approximate the region bounded by y=-x^3 and y=-x Show that the function f(x)= (integral from 2x to 5x) (1)/(t) dt is constant on the interval (0,+infinity)

More Similar Questions