Evaluate the following iterated integrals. int_0^2int_0^1frac{8xy}{1+x^4}dxdy

Kye 2021-01-31 Answered
Evaluate the following iterated integrals.
02018xy1+x4dxdy
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Expert Answer

StrycharzT
Answered 2021-02-01 Author has 102 answers
The given integral is 02018xy1+x4dxdy
Evaluate the given integral as shown below:
02018xy1+x4=02y[018x1+x4dx]dy
Substitute u=x2,du=2xdx
02018xy1+x4dxdy=02y[018x1+x4dx]dy
=02y[4012x1+(x2)2dx]dy
=02y[401du1+u2dx]dy
=02y[4(tan1u)01]dy
=02y[4(tan11tan10)]dy
=02y[4(π/40)]dy
=02yπdy
=π[y22]02
=π[2220]02
=2π
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