定積分

(1)  ${\displaystyle {\int }_1^2\left(x^3-3x^2+\frac{1}{\sqrt{x}}\right)dx}$ を計算しなさい． ⇒ 解答

(2)  ${\displaystyle {\int }_{-\frac{\pi }{4}}^{\frac{\pi }{2}}sin\left(x+\frac{\pi }{2}\right)dx}$ を計算しなさい． ⇒ 解答

(3)  ${\displaystyle {\int }_2^4{e}^{\frac{1}{2}x}dx}$ を計算しなさい． ⇒ 解答

(4)  ${\displaystyle {\displaystyle {\int }_0^1\frac{x^2+1}{x+1}dx}}$ を計算しなさい． ⇒ 解答

(5)  ${\displaystyle {\int }_1^{\sqrt{2}}\frac{1}{\sqrt{4-2x^2}}dx}$ を計算しなさい． ⇒ 解答

(6)  ${\displaystyle {\displaystyle {\int }_1^{e}x\log xdx}}$ を計算しなさい． ⇒ 解答

(7)  ${\displaystyle {\int }_0^6\left|\frac{x}{2}-1\right|dx}$ を計算しなさい． ⇒ 解答

(8)  ${\displaystyle {\int }_0^1\frac{x^5}{\sqrt{1-x^2}}dx}$ を計算しなさい． ⇒ 解答

(9)  ${\displaystyle {\int }_{\frac{1}{2}}^1\sqrt{1-x^2}dx}$ を計算しなさい． ⇒ 解答

(10)  ${\displaystyle {\displaystyle {\int }_0^{\frac{\pi }{2}}{\sin }^{n}xdx}}$ を計算しなさい． ⇒ 解答

(11)  ${\displaystyle {\displaystyle {\int }_0^{\frac{\pi }{2}}{\cos }^{n}xdx}}$ を計算しなさい． ⇒ 解答