Integral Calculus

Show that gamma(1/2)=sqrt(pi) Question Question Show that gamma(1/2)=sqrt(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 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) Evaluate integral of (1/(1+x^4)) dx…

Beta and Gamma Functions By means of integral there are two special functions namely Beta function and Gamma function. These functions help us to evaluate certain definite integrals which are sometimes difficult or impossible to evaluate by other known methods of integration. 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…

Applications of Double Integrals and Triple Integrals With the knowledge of double and triple integrals, we can find Area, Volume and Centre of gravity of different objects. Formula to find Area and Volume Formula to find the Centre of gravity 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…

Types of Evaluation of Double Integral The double integral can be evaluated in three different ways Topic Types of Evaluation of Double Integral Problems Evaluate double integral of xy dx dy over the specified region R, where R is the region bounded by the coordinate axes and the line x+y=1 Evaluate double integral of [xy(x+y) dy dx ] taken over the area between y=x^2 and y=x Evaluate double integral of xy dx dy over the positive quadrant of the circle…

Double Integral Problems Evaluate double Integral of xy dy dx over the limits y=(x, sqrt(x)) and x=(0,1) Evaluate double Integral of (x^2 +y^2) dy dx over the limits y=(x, sqrt(x)) and x=(0,1) Evaluate the double integral of xy dy dx over the limits for y= (x^2 to 2-x) and x=(0 to 1) Evaluate the double integral of (dy dx) / (1+x^2+y^2) over the limits y = (0 to sqrt(1+x^2) and x = (0 to 1) Triple Integral Problems Evaluate triple…