问一道e^(x^2)重积分的题目∫(0,1)[∫(3y,3) e^x2 dx]dy

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问一道e^(x^2)重积分的题目∫(0,1)[∫(3y,3) e^x2 dx]dy

问一道e^(x^2)重积分的题目∫(0,1)[∫(3y,3) e^x2 dx]dy
问一道e^(x^2)重积分的题目
∫(0,1)[∫(3y,3) e^x2 dx]dy

问一道e^(x^2)重积分的题目∫(0,1)[∫(3y,3) e^x2 dx]dy
是4/3e3

交换积分顺序:
=∫(0,3)[∫(0,x/3)e^(x^2)dy]dx
=∫(0,3)[ye^(x^2) | (0,x/3)]dx
=1/3 * ∫(0,3)xe^(x^2)dx
=1/6 * ∫(0,3)e^(x^2)d(x^2)
=1/6 * e^(x^2)|(0,3)
=1/6 * [e^9-1]