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The integral $\int_{0}^{1}\left(5 x^{3}+4 x^{2}+3 x+2\right) \mathrm{d} x$ is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statements is TRUE?
(A) Simpson's rule as well as rectangular rule of estimation will give NON-zero error.
(B) Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
(C) Only the rectangular rule of estimation will give zero error.
(D) Only Simpson's rule of estimation will give zero error.


Question ID - 157229 | Toppr Answer

The integral $\int_{0}^{1}\left(5 x^{3}+4 x^{2}+3 x+2\right) \mathrm{d} x$ is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statements is TRUE?
(A) Simpson's rule as well as rectangular rule of estimation will give NON-zero error.
(B) Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
(C) Only the rectangular rule of estimation will give zero error.
(D) Only Simpson's rule of estimation will give zero error.

1 Answer - 5876 Votes

3537

Answer Key : (D) -

Only Simpson's rule of estimation will give zero error.



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