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Moving Across the Coordinate Plane May 13, 2011

Posted by Billy in : calculus , add a comment

Albert is standing at the origin of the Cartesian plane, desperately in need of cake. Looking around, he spots some delicious chocolate cake at the point $(100,100)$. Albert immediately departs for the cake. He knows that if he goes outside the square with corners $(0,0)$, $(100,0)$, $(100,100)$, and $(0,100)$ the cake will disappear and he will starve. When Albert is at the point $(x,y)$, the maximum speed he can move is given by $v(x,y) = 5+\frac{y}{20}$. What is the minimum time required for Albert to reach the cake?

A Tricky Exponent March 25, 2011

Posted by Saketh in : calculus , 1 comment so far

Determine the exact value of  $$\int^{\frac{\pi}{2}}_0 \frac{1}{1+(\tan{x})^{\sqrt{2}}} \,dx$$

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An Integral March 25, 2011

Posted by Arjun in : calculus , 3 comments

Find $$\int^{\frac{\pi}{2}}_0 \frac{1}{\sqrt{\tan{x}}} \,dx$$