BE Biotechnology छमाही २ (इंजीनियरिंग) - University of Mumbai Important Questions for Applied Mathematics 2

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

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

Find the value of the integral `int_0^1 x^2/(1+x^3`𝒅𝒙 using Trapezoidal rule

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

Find the perimeter of the curve r=a(1-cos 𝜽)

Change the order of integration and evaluate `int_0^1 int_x^sqrt(2-x^2 x  dx  dy)/sqrt(x^2+y^2)`

Show that `int_0^asqrt(x^3/(a^3-x^3))dx=a(sqrtxgamma(5/6))/(gamma(1/3))`

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` usingTrapezoidal rule by dividing into six Subintervals.

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

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

Evaluate I = `int_0^1 int_0^(sqrt(1+x^2)) (dx.dy)/(1+x^2+y^2)`

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

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

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

Find the area inside the circle r=a sin𝜽 and outside the cardioide r=a(1+cos𝜽 )

Find the volume of the paraboloid `x^2+y^2=4z` cut off by the plane 𝒛=𝟒

Evaluate `int int int sqrt(1-x^2/a^2-y^2/b^2-x^2/c^2 )`dx dy dz over the ellipsoid `x^2/a^2+y^2/b^2+z^2/c^2=1.`

Evaluate `int int xy(x-1)dx  dy` over the region bounded by 𝒙𝒚 = 𝟒,𝒚= 𝟎,𝒙 =𝟏 and 𝒙 = 𝟒

Evaluate `int int(2xy^5)/sqrt(x^2y^2-y^4+1)dxdy`, where R is triangle whose vertices are (0,0),(1,1),(0,1).

Find the volume enclosed by the cylinder `y^2=x` and `y=x^2` Cut off by the planes z = 0, x+y+z=2.