Question

In Exercises 1-6, (a) use the Trapezoidal Rule with n = 4 to approximate the value of the integral, (b) Use the concavity of the function to predict whether the approximation is an overestimate or an underestimate. Finally, (c) find the integral's exact value to check your answer. rada

Answer 1

We hawe to approximate the value of onligral nia sapzoidal rule Let y = x2 , n = 4. We know thada Soy da ~ h [% + 2/7, + Ya + - + Yor) + Yor] h bra, nere a b=2,.. h = 20 = 1 = 0.5 Y©) = 70-5) = 0.25- y0 = 1 7 (15) = 2.25 and y(2) = 4. By Trapzoidal rules Sadxa 05/0+2(0.25 +1 +2.25 +4] -=[ 0.50 +2+ 4.50 +47 = [ 1 ] = 4 = 2.75 .: Serdam 2.75

(6) Graph of y: x², . concave up lyx | 4y= 22 Do x Anea (BDC) = 1.2x 4 = 4. (C) I = S 22 dx = 6332 - 2.67 8 Approximale value of legral is overestimated. Let the population proportitas be land. sample proportion ke p. So the confidence lênal for pas 100 (1-0)%0 confidence level is given by ? C1 = Č I TX PCIP) - ① from equation or we can say that for obtaining CI for Pn We Weed only sauple proportion. & level of sigufiecure. I