Question

求高等数学大神帮忙解答..

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Answer 1

3. f'(x)=3x^2+a
f'(1)=3+a=0 a=-3
f'(x)=3x^2-3=0
x=±1
极大值 f(-1)=5
极小值 f(1)=1
4. 原式=∫(x^(3/2)-x^(1/2))dx=(2/5)x^(5/2)-(2/3)x^(3/2)+C
5.原式=π-∫[0,π](1-sin^2(x))dsinx=π-[sinx-sin^3(x)/3]|[0,π]=π

Answer 2

3.f'(x)=3x^2+a 3+a=0 a=-3
f'(x)=3x^2-3 令 f'(x)=0 得 x=1 x=-1 极值：f(1)=1-3+3=1 f(-1)=-1+3+3=5
4. 原式=∫[x^(3/2)+2x+x^(1/2)]dx=2/5x^(5/2)+x^2+2/3x^(3/2)+C
5.原式=x[0,π]-∫[1-(sinx)^2]dsinx
=π-sinx[0,π]+1/3(sinx)^3[0,π]
=π

Answer 3

3. f(x)导数为：3x^2+a,令3x^2+a=0且x=1,解得a=-3.
所以f(x)=x^3-3x+3，令f(x)的导数等于0，解得：x=1，-1

4.把不定积分展开得：∫ x^3/2 +x^1/2 dx=2/5 x^5/2 -2/3 x^3/2 +C.

5.变换cos^3 x dx=(cos^2 x )d(sinx)=(1-sin^2 x )d(sinx)
原式=∫（0到π）1 dx 减去 ∫ (0到π)=(1-sin^2 x )d(sinx)
=π 减去 （sinx-1/3 sin^3 x）(0到π)
=π -0
=π

Answer 4

1.a=-3
f(1)=1,f(-1)=5
2. 2/5x^(5/2)-2/3x^3/2 +c
3.0

Answer 5

见图（用专用软件做的慢了点）