What is the integral from x^2 to 4-x^2 of y ?

The integral from x^2 to 4-x^2 of y is 4(-x^2+2)

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

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

4 (- x^{2} + 2)

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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

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)

What is the integral from x^2 to 4-x^2 of y ?
The integral from x^2 to 4-x^2 of y is 4(-x^2+2)