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 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 [FONT=verdana](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.