Find each double integral. Show all steps.
1.) int[0,1] int[x,e^x] 3 xy^2 dy dx
2.) int[0,squareroot(pi/6)] int[0,X] cos(x^2) dy dx
1.) int[0,1] int[x,e^x] 3 xy^2 dy dx
2.) int[0,squareroot(pi/6)] int[0,X] cos(x^2) dy dx
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Go to wolfram they show the steps clearly and I don't feel like typing a lot of symbols
1. do first int you'll get int[0,1] 1/3xe^(3x)- 1/3x^4
two terms the first one 1/3xe^(3x) have to do by integration by parts - int[0,1]1/3x^4 is easy = -1/15
the one by parts u=x dv=e^3x du=dx v = 1/3e^3x
...... lots more writing you get the answer (2e^3)/27 - 4/135
2. first integral easy, get int[0,squareroot(pi/6)] xcos(x^2) dx
then u substitution u=x^2 answer is 1/4
1. do first int you'll get int[0,1] 1/3xe^(3x)- 1/3x^4
two terms the first one 1/3xe^(3x) have to do by integration by parts - int[0,1]1/3x^4 is easy = -1/15
the one by parts u=x dv=e^3x du=dx v = 1/3e^3x
...... lots more writing you get the answer (2e^3)/27 - 4/135
2. first integral easy, get int[0,squareroot(pi/6)] xcos(x^2) dx
then u substitution u=x^2 answer is 1/4