1)Find the area of the region bounded by the curves y = x and y = sin(x) and the

Question

1)Find the area of the region bounded by the curves y = x and y = sin(x) and the lines x = 0 and x = pi/2 2)Use the Trapezoidal Rule with n = 2 to approximate the integral 1,0) x^3 dx. 3)What is the difference between calculating the integral (1,0) x^3 dx explicity and approximating it by using the Trapezoidal Rule with n = 2? 4)What is the upper bound for the error in approximating the integral(1,0) x^3 dx by using the Trapezoidal Rule with n = 2. 5)How large should n, the number of intervals, be in order to guarantee R that the Trapezoidal Rule approximation for integral (1,0) x^3 dx be accurate to within 0.0001?

Explanation / Answer

1) Area = Integral (x=0 to pi/2) Sin (x) dx = -(Cos (pi/2) - Cos(0)) = -(0 - 1) = 1

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