Category 21MAT21

Evaluate ∫√𝑐𝑜𝑠𝜃𝑑𝜃 by taking 7 ordinates by Simpson’s 1/3 rd rule

7.C] Evaluate by taking 7 ordinates by Simpson’s 1/3 rd rule.

7.B] Using Newton’s forward interpolation find y at x = 5 from the data:- x 4 6 8 10 y 1 3 8 16

6.B] Solve = sin 𝑥 sin 𝑦 for which = −2 sin 𝑦 when x= 0 and z = 0 when y is odd multiple of .

1.B] Find the volume bounded by the cylinder 𝑥2 + 𝑦2 = 4 and the planes 𝑦 + 𝑧 = 4 and 𝑧 = 0, by using double integration

10 c] Applying Milnes Predictor – Corrector method, to find y(1.4), from given that y(1)=2, y(1.1)=2.2156, y(1.2)=2.4549, y(1.3)=2.7514

10 b] Using the Runge-Kutta method of order 4, find y at x=0.1, given that ,y(0)=1

10 a] Employ Taylors series method to evaluate y(0.2), taking h=0.1 from , with y(0)=1

9 c] Applying Milne’s Predictor-Corrector method for given equation, find y(0.8), from , given that y(0)=2, y(0.2)=2.073, y(0.4)=2.452, y(0.6)=3.023

9 b] By using modified Euler’s method, find y(0.2), taking h=0.1 from , with y(0)=1

9 a] Use the Taylor series method to find 𝑦(0.2) from , with y(0)=1