Recent content by Blandongstein

Let $A_r(r \in \mathbb{N})$ be the area of the bounded region whose boundary is defined by $(6y^2r-x)(6\pi^2 y-x)=0$ then find the value of $$ \lim_{n \to \infty}(\sqrt{A_1 A_2 A_3}+\sqrt{A_2 A_3 A_4}+\cdots \text{n terms})$$

Let $f$ be a continuous function for $x \in (0,1]$ and $\displaystyle g(x)=\int_{1}^{1 \over x}\frac{1}{t}f\left( \frac{1}{t}\right)dt$, then find the value of $$ \int_0^1 (f(x)-g(x))dx$$

Homework Statement A water droplet starts falling from rest from a height h and a quires the terminal speed just before reaching the ground. If g(acceleration due to gravity) is assumed to be constant and the radius of the drop is r, find the work done by air drag. The density of air is...

Homework Statement A tube of uniform cross-section A is bent to form a circular arc of radius R, forming three quarters of a circle. A liquid of density \rho is forced through the tube with a linear speed v. Find the net force exerted by the liquid on the tube. 2. The attempt at a solution...

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Find the area of the polygon formed by the points (3,5), (5,11), (14,7), (8,3), and (6,6). I can find the area of the polygon by dividing it into 3 triangles and then finding area of each triangle separately. I want to know if there is any simpler way of doing this.

\[ \int \sin^{12}(7x) \ \cos^{3}(7x) \ dx \] Ho do I solve this Integral? What can I substitute??

I found this question on a website. Homework Statement Prove that \displaystyle \int_{0}^{\pi}\frac{1-\cos(nx)}{1-\cos(x)} dx=n\pi \ \ , n \in \mathbb{N} 2. The attempt at a solution Here's my attempt using induction: Let P(n) be the statement given by...

The area of an irregular quadrilateral is A= \sqrt{(s-a)(s-b)(s-c)(s-d)-abcd\cdot\cos^2{\frac{\alpha +\gamma}{2}}} where a,b,c,d are the sides. s is the semi-perimeter and \alpha and \gamma are any two opposite angles.