NettetA = \pi r^2, A = πr2, where A A is the area of a circle and r r is the radius. V = \frac {4} {3}\pi r^3, V = 34 πr3, where V V is the volume of a sphere and r r is the radius. SA = 4\pi r^2, S A = 4πr2, where SA S A is the surface area of a sphere and r r is the radius. A = \pi a b, A = πab, where A A is the area of an ellipse and a a and Nettet30. mar. 2024 · Ex 7.10, 5 - Chapter 7 Class 12 Integrals (Term 2) Last updated at March 30, 2024 by Teachoo. Get live Maths 1-on-1 Classs - Class 6 to 12. Book 30 minute class for ₹ 499 ₹ 299. Transcript. Show More. Next: Ex 7.10, 6 → Ask a doubt . Chapter 7 Class 12 Integrals; Serial order wise;

Integral sin(x^2) from 0 to infinity - YouTube

NettetUse Green's Theorem to calculate the area of the disk D of radius r defined by x 2 + y 2 ≤ r 2. Solution: Since we know the area of the disk of radius r is π r 2, we better get π r 2 for our answer. The boundary of D is the circle of radius r. We can parametrized it in a counterclockwise orientation using c ( t) = ( r cos t, r sin t), 0 ≤ t ≤ 2 π. Nettet30. apr. 2024 · Hence, I = Re [ π 2√e] = π 2√e. In solving the integral this way, we must close the contour in the upper half-plane because our choice of complex integrand was bounded in the upper half-plane. Alternatively, we could have chosen to write I = Re∫∞ − ∞dx e − ix 4x2 + 1, i.e., with e − ix rather than eix in the numerator. half moon shaped windows

A question in Complex Analysis $\\int_0^{2\\pi}\\log(1-2r\\cos x …

NettetWe have 1 − 2rcosx + r2 = (1 − reix)(1 − re − ix) = 1 − reix 2. Hence the integral can be written 2∫2π 0 log 1 − reix dx = 4π ⋅ 1 2π∫2π 0 log 1 − reix dx = 2 i∫γrlog 1 − z z … NettetThe area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding … NettetIn mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, … half moon shawl crochet pattern