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Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Problem Question Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Using the…

Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Problem Question Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Using the concept of orthogonal trajectories show that…

Find the orthogonal trajectories of the family r=a(1+sin(theta)) Question Question Find the orthogonal trajectories of the family r=a(1+sin(theta)) Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Using the concept of orthogonal trajectories show that…

Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Question Question Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family…

Find the Centre of gravity in the shape of the asteroid x^(2/3) –y^(2/3) = a^(2/3) represented in the first quadrant Question Question Find the Centre of gravity in the shape of the asteroid x^(2/3) –y^(2/3) = a^(2/3) represented in the first quadrant Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the…

Find the centre of gravity of the triangular lamina bounded by the coordinate axes and the line x/a + y/b =1 Question Question Find the centre of gravity of the triangular lamina bounded by the coordinate axes and the line x/a + y/b =1 Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π…

Show that beta(m,n) = integral of (x^(m-1)/(1+x)^(m+n)) dx over the limits (0 to infinity) Question Question Show that beta(m,n) = integral of (x^(m-1)/(1+x)^(m+n)) dx over the limits (0 to infinity) Topic Beta and Gamma Functions Independent Proof of Gamma Function - Show that gamma(1/2)=sqrt(pi) Beta and Gamma Function Problems Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by…

Evaluate integral of (1/(1+x^4)) dx over the limits (0 to infinity) Question Question Evaluate integral of (1/(1+x^4)) dx over the limits (0 to infinity) Topic Beta and Gamma Functions Independent Proof of Gamma Function - Show that gamma(1/2)=sqrt(pi) Beta and Gamma Function Problems Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function…

Evaluate integral of (4-x^2)^(3/2) dx over the limits (0 to 2) Question Question Evaluate integral of (4-x^2)^(3/2) dx over the limits (0 to 2) Topic Beta and Gamma Functions Independent Proof of Gamma Function - Show that gamma(1/2)=sqrt(pi) Beta and Gamma Function Problems Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function…

Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function Question Question Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function Topic Beta and Gamma Functions Independent Proof of Gamma Function - Show that gamma(1/2)=sqrt(pi) Beta and Gamma Function Problems Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Evaluate integral of sqrt(cot(theta))…

Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Question Question Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Topic Beta and Gamma Functions Independent Proof of Gamma Function - Show that gamma(1/2)=sqrt(pi) Beta and Gamma Function Problems Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi Evaluate integral…

Find the volume of the solid bounded by the planes x=0, y=0, z=0, x+y+z=1 Question Question Find the volume of the solid bounded by the planes x=0, y=0, z=0, x+y+z=1 Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial…

Find the volume bounded by the cylinder x^2+y^2=4 and the planes y+z=4, z=0 Question Question Find the volume bounded by the cylinder x^2+y^2=4 and the planes y+z=4, z=0 Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial line Find…

Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial line Question Question Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial line Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about…

Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Question Question Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the volume generated by the revolution of the Cardioids…

Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Question Question Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Topic Applications of Double Integrals and Triple Integrals Problems Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial line Find the volume bounded by…