演習問題

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }\left(2xy+3y^2\right)dxdy}$　　${\displaystyle \left(D:x^2\leqq y\leqq x\right)}$

次の数値を簡単な ${\displaystyle a^r}$ の形にせよ ．

${\displaystyle \frac{1}{\sqrt[3]{512}}}$

次の式を簡単にせよ．

${\displaystyle -3^2+{\left(-2\right)}^5+8^{\frac{1}{3}}+2^3\cdot 2^2}$

関数 ${\displaystyle f(x)=A{e}^{-bx}}$ が次を満たすとき， $A$ ， $b$ を求めよ．

${\displaystyle f(0)=4}$ ， ${\displaystyle f(2)=1}$

${\displaystyle {log}_{\frac{1}{2}}32}$

${\displaystyle {log}_2\left(\frac{1}{\sqrt{8}}\right)}$