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A 2nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $$\int\limits_0^2 {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$   is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as "true value - approximate value") in the estimate?

A 2nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $$\int\limits_0^2 {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$   is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as "true value - approximate value") in the estimate? Correct Answer $$ - \frac{4}{3}$$

Related Questions

The integral $$\int\limits_{{{\text{x}}_1}}^{{{\text{x}}_2}} {{{\text{x}}^2}{\text{dx}}} $$  with x2 > x1 > 0 is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $$I$$ is the exact value of the integral obtained analytically and J is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?
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Complex Variable mcq question image
The value of $$I$$ is
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