What is the integral from-x^2 to x^2+1 of f(x,y) ?

The integral from-x^2 to x^2+1 of f(x,y) is f,x(((1+x^2)^2)/2-(x^4)/2)

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integral from-x^2 to x^2+1 of f(x,y)

\int_{- x^{2}}^{x^{2} + 1} f (x, y) d y

f, x (\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2})

Solution steps

\int_{- x^{2}}^{x^{2} + 1} f (x, y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= f \cdot \int_{- x^{2}}^{1 + x^{2}}, x y d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= f, x \cdot \int_{- x^{2}}^{1 + x^{2}} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{- x^{2}}^{1 + x^{2}}

= f, x [\frac{y ^{2}}{2}]_{- x^{2}}^{1 + x^{2}}

Compute the boundaries:

\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2}

= f, x (\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2})

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What is the integral from-x^2 to x^2+1 of f(x,y) ?
The integral from-x^2 to x^2+1 of f(x,y) is f,x(((1+x^2)^2)/2-(x^4)/2)