The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.
Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]
The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad {(rounded off to 2 decimal places)}. \]
The table below gives values of the function \( f(x) = \frac{1}{x} \) at 5 points of \( x \).} \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 1.25 & 1.5 & 1.75 & 2 \\ \hline f(x) & 1 & 0.8 & 0.6667 & 0.57143 & 0.5 \\ \hline \end{array} \] The approximate value of \( \int_1^2 \frac{1}{x} \, dx \) using Simpson’s \( \left( \frac{1}{3} \right) \)rd rule is:
The table below gives the values of \( f(x) \) at five equidistant points of \( x \):
Then the approximate value of \( \int_0^2 f(x) \, dx \) by Trapezoidal Rule is:
The quadrature formula \[ \int_0^2 x f(x) \, dx \approx \alpha f(0) + \beta f(1) + \gamma f(2) \] is exact for all polynomials of degree \( \leq 2 \). Then \( 2 \beta - \gamma = \underline{\hspace{1cm}} \).
Value of \( \int_4^{5.2} \ln x \, dx \) using Simpson's one-third rule with interval size 0.3 is
