Using the Trapezoidal Rule with n = 3, the approximated value of $\int _ { - 1 } ^ { 0 } \frac { 1 } { \sqrt { 1 - x ^ { 3 } } } d x,$ to three decimal places, is

A)1.357
B)1.216
C)0.905
D)0.894
E)0.978

Question

Using the Trapezoidal Rule with n = 3, the approximated value of $\int _ { - 1 } ^ { 0 } \frac { 1 } { \sqrt { 1 - x ^ { 3 } } } d x,$ to three decimal places, is

A)1.357
B)1.216
C)0.905
D)0.894
E)0.978

Quizplus · Accepted Answer

The Trapezoidal Rule approximates the integral by dividing the interval into n subintervals, calculating the function value at each endpoint, and averaging. With n=3, the interval [-1,0] is divided into three subintervals. Calculating the function values at these points and applying the Trapezoidal Rule formula gives an approximation of 0.905.

Using the Trapezoidal Rule with N = 3, the Approximated ∫−1011−x3dx,\int _ { - 1 } ^ { 0 } \frac { 1 } { \sqrt { 1 - x ^ { 3 } } } d x,∫−10​1−x3​1​dx,

Using the Trapezoidal Rule with N = 3, the Approximated $\int _ { - 1 } ^ { 0 } \frac { 1 } { \sqrt { 1 - x ^ { 3 } } } d x,$