i don't get why the answer starts with (-1/3)?
How?
更新1:
i dont get the second step
更新2:
du/-2?
更新3:
du/-2?
更新4:
please also explain -1/2 * [2/3 * u^(3/2)] + C -1/3*(4 - x^4)^(3/2) + C
What is the integration of (2x^3)sqrt(4-x^4) dx, u = 4-x^4?
2011-10-20 3:31 am
What is the integration of (2x^3)sqrt(4-x^4) dx, u = 4-x^4?
i don't get why the answer starts with (-1/3)?
How?
i don't get why the answer starts with (-1/3)?
How?
回答 (2)
2011-10-20 3:37 am
✔ 最佳答案
-1/3 (4-x^4)^(3/2) + CEdit: actually its du/-4 and then you divide by two and it becomes du/-2.
it come from U = 4-x^4, then du - -4x^3, dx = -1/4du
2011-10-20 3:37 am
∫(2x^3)*√(4 - x^4) dx
u = 4 - x^4
du/-2 = 2x^3 dx
-1/2*∫√u du
-1/2 * [2/3 * u^(3/2)] + C
-1/3*(4 - x^4)^(3/2) + C
Does that perhaps answer your question?
u = 4 - x^4
du/-2 = 2x^3 dx
-1/2*∫√u du
-1/2 * [2/3 * u^(3/2)] + C
-1/3*(4 - x^4)^(3/2) + C
Does that perhaps answer your question?
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