PYQs Based Test - 27 : Numerical Methods (Integral Equations)

Numerically integrate, f(x) = 10x - 20x² from lower limit a = 0 to upper limit b = 0.5. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is ______.

The error in numerically computing the integral ${\int }_0^{\pi }\left(\sin x+\cos x\right)dx$ using the trapezoidal rule with three intervals of equal length between 0 and π is _______

P (0, 3), Q (0.5, 4), and R (1, 5) are three points on the curve defined by. 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

For the integral ${\int }_0^{\pi /2}\left(8+4\cos x\right)dx,$ the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the endpoints, is ______

(round off to one decimal place).

The evaluation of the definite integral ${\int }_{-1}^{1.4}x\left|x\right|dx$ by using Simpson’s 1/3${}^{rd}$ (one –third) rule with step size h = 0.6 yields