来自李柏林的问题
【高数,设f(x)=∫0→x2xsintdt,求f(x)″积分后面那是0到x的平方答案是6xsinx^2+4x^3cosx^2】
高数,设f(x)=∫0→x2xsintdt,求f(x)″
积分后面那是0到x的平方答案是6xsinx^2+4x^3cosx^2
1回答
2020-05-20 14:32
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蒋艳
因为f(x)=∫xsintdt,所以
f(x)=-xcost+c|
=-xcos(x²)+c-(-xcos0+c)
=x-xcos(x²)
所以：f'(x)=1-cos(x²)+2x²sin(x²)
f"(x)=[-cos(x²)]’+[2x²sin(x²)]’
=sin(x²)*2x+[2x²]’sin(x²)+2x²[sin(x²)]’
=2xsin(x²)+4xsin(x²)+2x²cos(x²)[(x²)]’
=2xsin(x²)+4xsin(x²)+4x³cos(x²)
=6xsin(x²)+4x³cos(x²)
2020-05-20 14:33:09