integral from x^2 to 4-x^2 of y

解答

\int_{x^{2}}^{4 - x^{2}} y d y

4 (- x^{2} + 2)

求解步骤

\int_{x^{2}}^{4 - x^{2}} y d y

使用幂法则

= [\frac{y ^{2}}{2}]_{x^{2}}^{4 - x^{2}}

带入上下限计算后得:

\frac{( 4 - x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2}

= \frac{( 4 - x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2}

化简

= 4 (- x^{2} + 2)

\int \frac{1}{( x ^{2} + 4 ) ^{\frac{5}{2}}} d x

d er i v a t i v e y = 2 x e^{- 3 x} + 3 e^{x^{2}}

y^{^{''}} = 3 t^{2}

\int e^{(- s t)} d t

y^{^{''}} + 4 y = sin (3 x)