Mathematics
Senior High
（2）ですお願いします
練習
222
***
次の定積分を求めよ。
(1) S₂1x²-x-2\dxx
2
@s.
10
(6x²+8x+3)dx
ESS
(2) a=
√√3-1
2
とすると,
√3-1
2 (6x²+8x+3) dx
Jo
=S₁ (6x² + 8x + 3) dx
= 2x³+4x²+3x
=2a³+4a²+3a
α
0
64
√3-1
ここで, α=
より、
2
両辺を2乗して整理すると,
このとき.
2a+1=√3
2a²+2a-1=0
2a³+4a²+3a=(2a²+2a-1)(a +1)+2a+1
=2a +1
よって,
√3-1
2(√3-1) +1
(6x²+8x+3)dx=2a+1=2(
= √3
(2a + 1)²=(√3)²
4a²+4a+1=3
4a²+4a-2=0
2a²+2a-1=0
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