# 2015 Countdown Problem #19: Find the Largest - Part III

Calculus Level 3

Which of the following is largest?

A. The value of $$\alpha$$ given that $\int _{ 0 }^{ \frac { \pi }{ 4 } }{ \tan ^{ \alpha }{ x } \mbox{ } \sec ^{ 2 }{ x } \mbox{ } dx } =\frac { 1 }{ 2015 }$

B. The value of $$\beta$$ given that $\int _{ 0 }^{ \beta }{ (round\left( x \right) +\left\lceil x \right\rceil -\left\lfloor x \right\rfloor -x)\mbox{ } dx } =2015$

C. The value of $$\gamma$$ given that $$\gamma$$ is the area bounded by the three straight lines represented by the equation $(y+3x+2015)(28x^2-xy+1540x-55y)=0$

D. The value of $$\delta$$ given that $\int { { (1-4060225{ x }^{ 2 }) }^{ -\frac { 1 }{ 2 } }\times { e }^{ (\sin ^{ -1 }{ 2015x } ) } \mbox{ } dx=\delta { e }^{ (\sin ^{ -1 }{ 2015x } ) }+C }$ where constant $$C \in \mathbb{R}$$

#MotherOfAllIntegrationProblems

This problem is part of the set 2015 Countdown Problems.

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