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The minimum number of equal length subintervals needed to approximate $$\int\limits_1^2 {{\text{x}}{{\text{e}}^{\text{x}}}{\text{dx}}} $$  to an accuracy of at least $$\frac{1}{3} \times {10^{ - 6}}$$  using the trapezoidal rule is

The minimum number of equal length subintervals needed to approximate $$\int\limits_1^2 {{\text{x}}{{\text{e}}^{\text{x}}}{\text{dx}}} $$  to an accuracy of at least $$\frac{1}{3} \times {10^{ - 6}}$$  using the trapezoidal rule is Correct Answer 1000e

Related Questions

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$
$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?
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?
The integral $$\int_1^3 {\frac{1}{{\text{x}}}{\text{dx,}}} $$   when evaluated by using Simpson's 1/3 rule on two equal subintervals each of length 1, equals
Aryan, Karan and Krishna have a few marbles with them 5 times the number of marbles Aryan has is equal to 4 times the number of marbles Karan has while 9 times the number of marbles Karan has is equal to 7 times the number of marbles Krishna has. What could be the minimum number of marbles with all three of them put together?
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With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
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II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
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$$\eqalign{ & {\text{The}}\,{\text{value}}\,{\text{of}} \cr & \frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}\,\text{is}: \cr} $$
The value of $$\left( {\frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}} \right)$$       is :