How do you find the error that occurs when the area between the curve $y = x^{3} + 1$ $y=x^3+1$ and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?

Question

How do you find the error that occurs when the area between the curve $y = x^{3} + 1$ $y=x^3+1$ and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?

1 Answer

Related questions

What is Integration Using the Trapezoidal Rule?
How does the trapezoidal rule work?
How do you Use the trapezoidal rule with four equal subdivisions to approximate a definite integral?
How do you Use the trapezoidal rule with $n = 10$ $n=10$ to approximate the integral $\int_{1}^{2} \frac{ln (x)}{1 + x} d x$ $int_1^2ln(x)/(1+x)dx$ ?
How do you Use the trapezoidal rule with $n = 6$ $n=6$ to approximate the integral $\int_{0}^{3} \frac{d x}{1 + x^{2} + x^{4}} d x$ $int_0^3dx/(1+x^2+x^4)dx$ ?
How do you Use the trapezoidal rule with $n = 10$ $n=10$ to approximate the integral $\int_{0}^{2} \sqrt{x} \cdot e^{- x} d x$ $int_0^2sqrt(x)*e^(-x)dx$ ?
How do you Use the trapezoidal rule with $n = 8$ $n=8$ to approximate the integral $\int_{0}^{π} x^{2} \cdot sin (x) d x$ $int_0^pix^2*sin(x)dx$ ?
How do you Use the trapezoidal rule with $n = 6$ $n=6$ to approximate the integral $\int_{0}^{1} e^{- \sqrt{x}} d x$ $int_0^1e^-sqrt(x)dx$ ?
When do you use the trapezoidal rule?
How do you solve the AP Calculus AB 2014 Free Response question #4?...

Impact of this question

3433 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-06T22:47:38

Assuming that you want the actual error, use the fundamental theorem of calculus to get the exact value of $\int_{0}^{1} (x^{3} + 1) d x$ $int_0^1(x^3+1)dx$ Then find the difference (subtract) from the trapezoid approximation.

I guess it's easy to see that
$\int_{0}^{1} (x^{3} + 1) d x = (\frac{x^{4}}{4} + x)]_{0}^{1} = (\frac{1}{4} + 1) - (0) = \frac{4}{5} = 1.25$ $int_0^1(x^3+1)dx=(x^4/4+x)]_0^1=(1/4+1)-(0)=4/5=1.25$ .
The trapezoid rule with $n = 4$ $n=4$ gives $1.265625$ $1.265625$

The error, then is $0.015625$ $0.015625$ .

Science

Math

Humanities

... and beyond

How do you find the error that occurs when the area between the curve $y = x^{3} + 1$ $y=x^3+1$ and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the error that occurs when the area between the curve y=x^3+1y=x3+1y=x^3+1 and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?

1 Answer

Related questions

Impact of this question

How do you find the error that occurs when the area between the curve $y = x^{3} + 1$ $y=x^3+1$ and the x-axis over the interval [0,1] is approximated by the trapezoid rule with n = 4?