Applied Mathematics – I

Aim: Procedure: 1. Indefinite Integrals. Output: output for indefinite integrals Function f(x) \[\int f(x)\ dx\] 5 5x x2 1/3 x3 ex ex sin x – cos x cos x sin x sec2x tan x 2. Definite Integrals. Output: output for definite integrals and area under the curve Function f(x) x = a x = b […]

Aim: Procedure: Output: Output for radius of curvature and length of the curve. Description Formula / Value Distance between parallels (V) V = 20 Distance between endpoint of the Inverse Curve (L) L = 200 Equation of the Circle c1 \[(x-0)^2\ +\ (y+480.12)^2\ = 250116.95\] centre of the Circle c1 F=(0,- 480.01) Radius of the

Aim: Procedure: Output: output to verify externally touching pitch circles Equation Center Radius Diameter Circle1 \[x^2\ +\ y^2\ =\ 3600\] c1 = (0,0) \[R_g\ =\ 60\] \[d_g\] = 120 Circle2 \[(x-70)^2\ +\ y^2\ =\ 100\] c2 = (70,0) \[R_p\] = 10 \[d_p\] = 20 Distance between centers c1c2 = 70 Sum of the Radii \[R_g\

Aim: Output: Output table for parabolic bridge Equation of the Parabola \[(x-3.4)^2\ =\ 4(-2.6)(y-1.5)\] Vertex (V) (3.4, 1.5) Focus (F) (3.4, – 1.1) Distance from vertex to focus 2.6 Directrix y = 4.1 latus rectum y = – 1.1 Height of the bridge 2.6 Width of the bridge 10.4

Syllabus: DIFFERENTIATION Sometimes y is not defined directly as a function of x but is given as a function of another variable, say ‘u’ which is defined as a function of x. Hence y is indirectly a function of x. In such case y is said to be a function of function. Successive Differentiation (Up