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{\large ���wI���K�@��X��@2007�N10��30���z�z} 

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�S�� ���n����CTA �O�p �~
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{\small

���K����
{\tt http://www.ms.u-tokyo.ac.jp/$\sim$hirachi/courses/sugaku-I-2007/}
����_�E�����[�h�ł��܂��D�u�`�������ڂ��Ă��܂��D
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{\bf ���.} $\varphi(x)$��$f(x)$��$\R$��̘A���֐��ł���
$\int_{-1}^{1}\varphi(x)dx=1$
����$|x|>1$�̂Ƃ�$\varphi(x)=0$�𖞂����Ƃ���B��������
$$
\lim_{h\to\infty} \int_{-1}^{1}h\varphi(x h)f(x)dx=f(0)
$$

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{\small
�ȉ��̖����ł���͈͂ŉ���, 11��6��13���܂łɃA�h�~�j�X�g���[�V�������̃��|�[�g��o�{�b�N�X�ɒ�o���邱��. 
}

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\prob 
�ȉ��̕s��ϕ������߂�B


(1) $\displaystyle\int \frac{x}{1+x+x^2+x^3}\ dx$.

(2) $\displaystyle\int\frac{1}{\sqrt{a^2-x^2}}\ dx, \qquad a>0.$

(3) $\displaystyle\int\frac{\cos^2x}{(\cos x +x\sin x)^2}\ dx$.


\prob ���R��$n$�ɑ΂��C
$$I_n=\int_0^{\pi/4}\tan^n x\;dx$$
�Ƃ����D���̒l�����߂�D

\prob ���$[-1,1]$��̘A���֐�$f(x)$�ɑ΂��C
$$\lim_{h\to 0+}\int_{-1}^1\frac{h}
{h^2+x^2}f(x)\;dx=\pi f(0)$$
�ł��邱�Ƃ������D



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