# calculus

444 views
The estimate of

$\int_{0.5}^{1.5}\frac{dx}{x}$

obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by

(A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012

reopened

1 vote
D option..
0
explain it
1
Find the actual value by integrating and putting it will be around 1.09861 .. Find value using simpson 3-point rule as h/3(y0+yn+4(y1+y3+...) +2(y2+y4+...)) it will be around 1.11111 Error=1.09861-1.11111 =0.012

## Related questions

1
281 views
Use Simpson's rule with $h=0.25$ to evaluate $V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or equal ... using the Simpson's rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
In questions 1.1 to 1.7 below, one or more of the alternatives are correct. Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up. 1.3 Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree 1 2 3 4