Approximate the given value using the Trapezoidal Rule with . Round to 3 decimal places.

Question

Approximate the given value using the Trapezoidal Rule with  . Round to 3 decimal places.

Quizplus · Accepted Answer

The Trapezoidal Rule for approximating a definite integral is given by:
Integral[a,b] f(x) dx ≈ (b-a) [(f(a)+f(b))/2]
Using this formula, with a=0, b=1, and f(x)= e^(x^2), we can plug in the values:
Integral[0,1] e^(x^2) dx ≈ (1-0) [(e^(0^2)+e^(1^2))/2] = (1/2) [(1+e)]= 0.859
Rounded to 3 decimal places, the answer is 0.859, which matches option C.

Approximate the Given Value Using the Trapezoidal Rule with