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MIT Integration Bee Qualifying Exam 24 January 2017

MIT Integration Bee Qualifying Exam24 January 20171 x2 x3+ 2dx2 1logxx2dx3 sech(x)dx4 x3ex2dx5 211x x2 1dx6 1dxx(x2+ 1)7 cosh 1xdx8 e 2x2 5x 3dx9 sin xdx10 0dx(x+ 1/x)211 (2 +x)e xx3dx12 10dx x(1 x)13 0tanh(x)exp(x)dx14 20 sin(x) + 1dx15limn In,whereI1= 10dx1 + x, I2= 10dx1 +11+ x, I3= 10dx1 +11+11+ x, ..16 sin2(x+ /4)ex2dx17 3x2(x3+ 1)2e x6 2x3dx18 /20dx1 + tan2017x19 e2xcos(3x)dx20 (cos(x))cos(x)+1tan(x)(1 + log(cos(x))dx)

MIT Integration Bee Qualifying Exam 24 January 2017 1 Z x2 p x3 +2 dx 2 Z 1 1 logx x2 dx 3 Z sech(x)dx 4 Z x3ex2 dx 5 Z 2 1 1 x p x2 1 dx 6 Z 1 1 dx x(x2 +1) 7 Z cosh 1 xdx 8 Z 1 1 e 2x2 5x 3 dx 9 Z sin p xdx 10 Z 1 0 dx (x+1=x)2

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