# GATE2016-2-29

The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ is ___________

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## Related questions

The values of function $f(x)$ at $5$ discrete points are given below: $\begin{array}{|l|l|l|l|l|l|} \hline x & 0& 0.1 & 0.2 & 0.3 & 0.4 \\ \hline f(x) & 0 & 10 & 40& 90 & 160 \\ \hline \end{array}$ Using Trapezoidal rule with step size of $0.1$, the value of $\int_{0}^{0.4}f(x)dx$ is __________
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________ (round off to one decimal place).
$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $x=0$ and $x=1$ for the curve. The difference between the two results will be $0$ $0.25$ $0.5$ $1$
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________