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

**Calculus**Level 3

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.*