计算定积分.定积分符号不好打,我就用区间直接表示了.1.函数(4-2x)(4-x^2)dx , [0,2]2.(x^2-2x-3)/x dx [1,2]3.(√x+1/√x)^2dx [2,3]4.√x（1-√x）dx [1,4]5.(3x+sinx)dx [0,2π]6.(e^x-2/x)dx [1,2] 1.e^2xdx [0,1]2.cos2xdx [π/6,π/4]3.2^xdx [1,3]就这些了,小弟刚接触定积分,不是很熟练,麻烦GGJJ帮帮忙...
∫(0~2) (4 - 2x)(4 - x^2) dx= ∫(0~2) (2x^3 - 4x^2 - 8x + 16) dx= 2 * x^4/4 - 4 * x^3/3 - 8 * x^2/2 + 16x |(0~2)= (1/2) * 2^4 - (4/3) * 2^3 - 4 * 2^2 + 16 * 2= 40/3∫(1~2) (x^2 - 2x - 3)/x dx= ∫(1~2) (x - 2 - 3/x) dx= x^2/2 - 2x - 3lnx |(1~2)= [1/2 * 2^2 - 2(2) - 3ln2] - [1/2 - 2 - 0]= - 1/2 - 3ln2∫(...全部
∫(0~2) (4 - 2x)(4 - x^2) dx= ∫(0~2) (2x^3 - 4x^2 - 8x + 16) dx= 2 * x^4/4 - 4 * x^3/3 - 8 * x^2/2 + 16x |(0~2)= (1/2) * 2^4 - (4/3) * 2^3 - 4 * 2^2 + 16 * 2= 40/3∫(1~2) (x^2 - 2x - 3)/x dx= ∫(1~2) (x - 2 - 3/x) dx= x^2/2 - 2x - 3lnx |(1~2)= [1/2 * 2^2 - 2(2) - 3ln2] - [1/2 - 2 - 0]= - 1/2 - 3ln2∫(2~3) (√x + 1/√x)^2 dx= ∫(2~3) (x + 2 + 1/x) dx= x^2/2 + 2x + lnx |(2~3)= [1/2 * 3^2 + 2(3) + ln3] - [1/2 * 2^2 + 2(2) + ln2]= 9/2 + ln(3/2)∫(1~4) √x * (1 - √x) dx= ∫(1~4) (√x - x) dx= (2/3)x^(3/2) - x^2/2 |(1~4)= [2/3 * 4^(3/2) - 1/2 * 4^2] - [2/3 - 1/2]= - 17/6∫(0~2π) (3x + sinx) dx= 3 * x^2/2 - cosx |(0~2π)= [3/2 * (2π)^2 - cos(2π)] - [0 - cos0]= 6π^2∫(1~2) (e^x - 2/x) dx= e^x - 2lnx |(1~2)= [e^2 - 2ln2] - [e - 0]= e^2 - e - 2ln2∫(0~1) e^(2x) dx= ∫(0~1) e^(2x) d(2x)/2= 1/2 * e^(2x) |(0~1)= [1/2 * e^2] - [1/2 * 1]= (e^2 - 1)/2∫(π/6~π/4) cos2x dx= (π/6~π/4) cos2x d(2x)/2= 1/2 * sin2x |(π/6~π/4)= [1/2 * sin(2 * π/4)] - [1/2 * sin(2 * π/6)]= (2 - √3)/4∫(1~3) 2^x dx= 2^x/ln2 |(1~3)= [1/ln2 * 2^3] - [1/ln2 * 2]= 6/ln2定积分不难,先求出不定积分,然后再把代入上限的原函数,减去代入下限的原函数就可以了。
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