Provide an appropriate response.
-Given that we know the Fundamental Theorem of Calculus, why would we want to develop numerical methods for definite integrals?
i) Antiderivatives are not always expressible in closed form.
ii) Numerical methods are a good excuse to use our graphics
calculator.
iii) The function f(x) may not be continuous on [a,b]
A) Only iii is correct.
B) Only ii is correct.
C) Only i is correct.
D) Both i and iii are correct.

Question

Quizplus · Accepted Answer

Antiderivatives are not always expressible in closed form, which makes it challenging to calculate exact values of definite integrals. In such cases, we can use numerical methods to approximate the value of the definite integral. Additionally, if the function f(x) is not continuous on [a,b], then the Fundamental Theorem of Calculus may not apply, and we need to resort to numerical methods to approximate the integral. However, the second option given, about using graphics calculators, is not a valid reason for developing numerical methods for definite integrals.

Provide an Appropriate Response