Question

suppose f(0.25)=f(0.75)=beta. find beta if the trapezium-rule with n=2 gives the value 2 for integral 0 to 1 f(x)dx and with n=4 gives the value 4

Answer 1

To find beta, we can set up two equations using the trapezium rule with different values of n. By solving these equations, we find that beta is equal to 1.6.

Step-by-step explanation:

To find the value of beta, we need to use the trapezium rule with different values of n (the number of subintervals). From the given information, when n=2, the value of the integral is 2, and when n=4, the value is 4. Let's use these values to set up two equations and solve for beta.

Since f(0.25)=f(0.75)=beta, we have:

2 = (0.5/2) * (beta + 2*beta + beta) = 1.5*beta

4 = (0.25/4) * (beta + 2*beta + 2*beta + 2*beta + beta) = 2.5*beta

Simplifying the equations, we get:

1.5*beta = 2

2.5*beta = 4

Dividing the second equation by 2.5, we find:

beta = 4/2.5 = 1.6

Therefore, beta is equal to 1.6.