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VTU 1st Year 21MAT21 [SET-2] Solved Model Question Paper Advanced Calculus and Numerical Methods

VTU 1st Year 21MAT21 Advanced Calculus and Numerical Methods set-2 Solved Model Question Paper with answers available on this website. VTU 1st Year Advanced Calculus and Numerical Methods set-2 Solved…

Change the order of integration and hence evaluate ∫∫𝑒^−𝑦/𝑦 𝑑𝑦𝑑x

2.A] Change the order of integration and hence evaluate dydx. Answer:-

Evaluate ∫∫𝑥𝑦 𝑑𝑥𝑑𝑦 over the region bounded by the x-axis, ordinate 𝑥=2𝑎 and the curve 𝑥^2 =4𝑎y

1.A] Evaluate ∫ ∫ 𝑥𝑦 𝑑𝑥𝑑𝑦 over the region bounded by the x-axis, ordinate x=2a and the curve 𝑥2 = 4𝑎y ANSWER:-

Evaluate ∫𝑑𝑥/1+𝑥^2, using Simpson’s (3/8) 𝑡ℎ rule by taking 7 ordinates.

8.C] Evaluate , using Simpson’s (3/8)𝑡ℎ rule by taking 7 ordinates. Answer:-

Show that ∫√sin𝜃/𝑑𝜃 ∫𝑑𝜃/√sin𝜃=π

1.C] Show that Answer:-

Solve by using Milne’s predictor-corrector method

10.C] Given , 𝑦(0) = 1, 𝑦(0.1) = 1.06, 𝑦(0.2) = 1.12, 𝑦(0.3)=1.21, evaluate 𝑦(0.4) by using Milne’s predictor-corrector method.

Show that 𝛤 (1/2 ) = √π

2.C] Show that .

Evaluate ∫ ∫ ∫ 𝑥𝑦𝑧 𝑑𝑥𝑑𝑦𝑑z

2.B] Evaluate xyz dxdydz.

Using the Newton-Raphson method, find the root of 3𝑥 = 𝑐𝑜𝑠𝑥+1 correct four decimal places.

8.A]Using the Newton-Raphson method, find the root of 3𝑥 = 𝑐𝑜𝑠𝑥 + 1 correct four decimal places.

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.