Use Simpson’s Rule with five ordinates to find an approximate value for the integral e^(x^2)dx between the values of 0 and 1

Find the value of dx by dividing the difference between the integral boundaries by the number of ordinates minus 1. Therefore dx=(1-0)/4=1/4. Then define your ordinates, by 5 values between 0 and 1, where the difference between them is 1/4. The ordinates for this example will therefore be 0, 0.25, 0.5, 0.75 and 1. Then use simpson's equation: (dx/3)(f(x0)+4f(x1)+2f(x2)+4f(x3)+f(x4)) by substituting your ordinate values into the original equation e^(x^2). If you typed everything into your calculator correctly, you should yield the answer 1.4637.

JF
Answered by Joshua F. Maths tutor

5852 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"


The velocity of a moving body is given by an equation v = 30 - 6t, where v - velocity in m/s, t - time in s. A) What is the acceleration a in m/s^2? B) Find the expression for the displacement s in terms of t given the initial displacement s(0)=10 m.


A curve has equation y = f(x) and passes through the point (4, 22). Given that f ′(x) = 3x^2 – 3x^(1/2) – 7, use integration to find f(x), giving each term in its simplest form.


A Curve has parametric equation x=2sin(t), y= 1+cos(2t), -pi/2<=t<=pi/2. a) Find dy/dx when t=pi/3. b) Find the Cartesian equation for the curve in form y=f(x), -k<=x<=k. c) Find the range of f(x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences