定積分の計算練習 220408
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ほぼ毎日の練習 220421
(1) \(\displaystyle{
\int_0^1
\dfrac{x}{\sqrt{x^2+4}}
\ dx
}\)
(2) \(\displaystyle{
\int_1^2
\dfrac{x^2-4x}{x^3-6x^2+1}
\ dx
}\)
(3) \(\displaystyle{
\int_1^\sqrt{3}
\dfrac{2x^3}{\sqrt{x^2+2}}
\ dx
}\)
(4) \(\displaystyle{
\int_1^4
\dfrac{(x-1)^2}{\sqrt{x}}
\ dx
}\)
(5) \(\displaystyle{
\int_1^{e^3}
\dfrac{(\log x)^2}{x}
\ dx
}\)
(6) \(\displaystyle{
\int_0^1
\dfrac{3x^2-5x+2}{3x+1}
\ dx
}\)
(7) \(\displaystyle{
\int_1^2
\dfrac{1}{2x-1}
\ dx
}\)
(8) \(\displaystyle{
\int_e^{e^3}
\dfrac{dx}{x\log x}
}\)
(9) \(\displaystyle{
\int_0^\frac{\pi}{4}
\dfrac{3+\cos^3 x}{\cos^2 x}
\ dx
}\)
(10) \(\displaystyle{
\int_\frac{\pi}{2}^{\pi}
\dfrac{\sin x}{1-\cos x}
\ dx
}\)
(11) \(\displaystyle{
\int_0^\sqrt{3}
\dfrac{dx}{\sqrt{4-x^2}}
}\)
(12) \(\displaystyle{
\int_{-7}^{-5}
\dfrac{dx}{(x+1)(x+4)}
}\)
(13) \(\displaystyle{
\int_0^\sqrt{2}
\dfrac{x^2}{2+x^2}
\ dx
}\)
(14) \(\displaystyle{
\int_{1}^{2}
x\sqrt{3x-2}
\ dx
}\)
(15) \(\displaystyle{
\int_{-\pi}^\pi
\sin^2 x
\ dx
}\)
(16) \(\displaystyle{
\int_{0}^{\pi}
\sqrt{1-\cos x}
\ dx
}\)
(17) \(\displaystyle{
\int_{0}^1
(1-x)e^x
\ dx
}\)
(18) \(\displaystyle{
\int_{0}^{1}
x\sqrt{1-x^2}
\ dx
}\)
(19) \(\displaystyle{
\int_{1}^e
x^2\log x
\ dx
}\)
(20) \(\displaystyle{
\int_{2}^{6}
\sqrt{2x-3}
\ dx
}\)
(21) \(\displaystyle{
\int_{0}^\frac{\pi}{2}
(2-\cos^2 x)\sin x
\ dx
}\)
(22) \(\displaystyle{
\int_{-\frac{\pi}{2}}^{0}
x\cos 3x
\ dx
}\)
(23) \(\displaystyle{
\int_{0}^\frac{\pi}{2}
x^2\sin x
\ dx
}\)
(24) \(\displaystyle{
\int_{-\frac{1}{2}}^{\frac{\sqrt{3}}{2}}
\sqrt{1-x^2}
\ dx
}\)
(25) \(\displaystyle{
\int_{-\frac{\pi}{3}}^\frac{\pi}{6}
\sin^3 x
\ dx
}\)
(26) \(\displaystyle{
\int_{0}^{\frac{\pi}{4}}
\sin 4x\cos 2x
\ dx
}\)
(27) \(\displaystyle{
\int_{1}^{e}
(\log x)^2
\ dx
}\)
(28) \(\displaystyle{
\int_{0}^{\frac{\pi}{2}}
e^{2x}\sin x
\ dx
}\)