BE Chemical Engineering सत्र २ (इंजीनियरिंग) - University of Mumbai Question Bank Solutions for Applied Mathematics 2

Solve `x^2 (d^2y)/dx^2+3x dy/dx+3y =(log x.cos (log x))/x`

Find by double integration the area bounded by the parabola 𝒚𝟐=𝟒𝒙 And 𝒚=𝟐𝒙−𝟒 

Solve  `xy(1+xy^2)(dy)/(dx)=1`

Change the order of integration of `int_0^1int_(-sqrt(2y-y^2))^(1+sqrt(1-y^2)) f(x,y)dxdy`

Find the value of the integral `int_0^1 x^2/(1+x^3`𝒅𝒙 using Simpson’s (1/3)^𝒕𝒉 rule.

Change the order of integration `int_0^aint_sqrt(a^2-x^2)^(x+3a)f(x,y)dxdy`

Using Modified Eulers method ,find an approximate value of y At x = 0.2 in two step taking h=0.1 and using three iteration Given that `(dy)/(dx)=x+3y` , y = 1 when x = 0.

Find the mass of a lamina in the form of an ellipse `x^2/a^2+y^2/b^2=1`, If the density at any point varies as the product of the distance from the
The axes of the ellipse.

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (1/3)^rd rule by dividing into six Subintervals.

Change the order of Integration and evaluate `int_0^2int_sqrt(2y)^2 x^2/(sqrtx^4-4y^2)dxdy`

Find the volume bounded by the paraboloid 𝒙^𝟐+𝒚^𝟐=𝒂𝒛 and the cylinder 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐. 

Change to polar coordinates and evaluate `int_0^1 int_0^x (x+y)dydx` 

Apply Rungee-Kutta Method of fourth order to find an approximate value of y when x=0.2 given that `(dy)/(dx)=x+y` when y=1 at x=0 with step size h=0.2.

Find the value of the integral `int_0^1 x^2/(1+x^3`𝒅𝒙 using Simpson’s (𝟑/𝟖)^𝒕𝒉 rule.

Evaluate `int_0^∞ 3^(-4x^2) dx` 

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (3/8)^th rule by dividing into six Subintervals.

Change the order of integration and evaluate `int_0^2 int_(2-sqrt(4-y^2))^(2+sqrt(4-y^2)) dxdy` 

Solve `dy/dx=x^3+y`with initial conditions y(0)=2 at x= 0.2 in step of h = 0.1 by Runge Kutta method of Fourth order. 

Solve `dy/dx+x sin 2 y=x^3 cos^2 y` 

Show that the length of curve `9ay^2=x(x-3a)^2  "is"  4sqrt3a`