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人気のある微分積分 >

integral from 4 to x^2 of (3t^2+2t)

解

\int_{4}^{x^{2}} (3 t^{2} + 2 t) d t

解

x^{6} + x^{4} - 80

解答ステップ

\int_{4}^{x^{2}} 3 t^{2} + 2 t d t

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{4}^{x^{2}} 3 t^{2} d t + \int_{4}^{x^{2}} 2 t d t

\int_{4}^{x^{2}} 3 t^{2} d t = x^{6} - 64

\int_{4}^{x^{2}} 2 t d t = x^{4} - 16

= x^{6} - 64 + x^{4} - 16

簡素化

= x^{6} + x^{4} - 80

人気の例

integral from 2 to e of 1/x

\int_{2}^{e} \frac{1}{x} d x

integral from 3 to 0 of (4x-x^3)

\int_{3}^{0} (4 x - x^{3}) d x

integral from 1/2 to 1/3 of cos(pix)

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (p i x) d x

integral from-2 to 2 of x(x^2-8)

\int_{- 2}^{2} x (x^{2} - 8) d x

integral from-2 to 2 of 10x^9+25x^7

\int_{- 2}^{2} 10 x^{9} + 25 x^{7} d x