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Find the value of the integral `int_0^1 x^2/(1+x^3`𝒅𝒙 using Simpson’s (1/3)𝒕𝒉 rule.
Concept: Numerical Integration‐ by Simpson’S 1/3rd
Find the perimeter of the curve r=a(1-cos 𝜽)
Concept: Rectification of Plane Curves
Change the order of integration and evaluate `int_0^1 int_x^sqrt(2-x^2 x dx dy)/sqrt(x^2+y^2)`
Concept: Differentiation Under Integral Sign with Constant Limits of Integration
Show that `int_0^asqrt(x^3/(a^3-x^3))dx=a(sqrtxgamma(5/6))/(gamma(1/3))`
Concept: Differentiation Under Integral Sign with Constant Limits of Integration
Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` usingTrapezoidal rule by dividing into six Subintervals.
Concept: Numerical Integration‐ by Trapezoidal
Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (1/3)rd rule by dividing into six Subintervals.
Concept: Numerical Integration‐ by Simpson’S 1/3rd
Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (3/8)th rule by dividing into six Subintervals.
Concept: Numerical Integration‐ by Simpson’S 3/8th Rule
Evaluate I = `int_0^1 int_0^(sqrt(1+x^2)) (dx.dy)/(1+x^2+y^2)`
Concept: Double Integration‐Definition
Change the order of integration of `int_0^1int_(-sqrt(2y-y^2))^(1+sqrt(1-y^2)) f(x,y)dxdy`
Concept: Change the Order of Integration
Change the order of integration `int_0^aint_sqrt(a^2-x^2)^(x+3a)f(x,y)dxdy`
Concept: Change the Order of Integration
Change the order of Integration and evaluate `int_0^2int_sqrt(2y)^2 x^2/(sqrtx^4-4y^2)dxdy`
Concept: Change the Order of Integration
Find the area inside the circle r=a sin𝜽 and outside the cardioide r=a(1+cos𝜽 )
Concept: Application of Double Integrals to Compute Area
Find the volume of the paraboloid `x^2+y^2=4z` cut off by the plane 𝒛=𝟒
Concept: Triple Integration Definition and Evaluation
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.`
Concept: Triple Integration Definition and Evaluation
Evaluate `int int xy(x-1)dx dy` over the region bounded by 𝒙𝒚 = 𝟒,𝒚= 𝟎,𝒙 =𝟏 and 𝒙 = 𝟒
Concept: Application of Double Integrals to Compute Area
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).
Concept: Application of Double Integrals to Compute Area
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.
Concept: Triple Integration Definition and Evaluation
Use polar co ordinates to evaluate `int int (x^2+y^2)^2/(x^2y^2)` 𝒅𝒙 𝒅𝒚 over yhe area Common to circle `x^2+y^2=ax "and" x^2+y^2=by, a>b>0`
Concept: Application of Double Integrals to Compute Area
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.
Concept: Application of Double Integrals to Compute Mass
Evaluate `int int intx^2dxdydz` over the volume bounded by planes x=0,y=0, z=0 and `x/a+y/b+z/c=1`
Concept: Application of Triple Integral to Compute Volume
