Question

计算下列定积分？

Answer 1

按照不定积分公式即可完成解答。

Answer 2

解如下图所示

Answer 3

(1)∫1/√XdX=2√X+C=2√2-2
(2)∫(³√X+1/X)dX=3/4X^(4/3)+㏑X+C
=3/4×3^(4/3)+㏑3-3/4×2^(4/3)-㏑2
=3/4(3׳√3-2׳√2)-㏑(3/2)
(3)∫e^2XdX=1/2∫e^2Xd2X=1/2×e^2X+C=1/2×e^2-1/2×e^0=1/2e^2-1/2

Answer 4

(1)
∫(1->2) dx/√x
= 2[√x]|(1->2)
=2(√2-1)
(2)
∫(2->3) [ x^(1/3) + 1/x] dx
=[(3/4)x^(4/3) + ln|x| ]|(2->3)
=[ (3/4)3^(4/3) + ln3 ] -[(3/4)2^(4/3) + ln2]
(3)

∫(1->2) e^(2x) dx
=(1/2)[e^(2x)]|(1->2)
=(1/2)(e^4 - e^2)