What is the integral from 0 to 1 of 12x^2y^3 ?

The integral from 0 to 1 of 12x^2y^3 is 3x^2

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integral from 0 to 1 of 12x^2y^3

\int_{0}^{1} 12 x^{2} y^{3} d y

3 x^{2}

Solution steps

\int_{0}^{1} 12 x^{2} y^{3} d y

Take the constant out:

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

= 12 x^{2} \cdot \int_{0}^{1} y^{3} d y

Apply the Power Rule

: [\frac{y ^{4}}{4}]_{0}^{1}

= 12 x^{2} [\frac{y ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= 12 x^{2} \frac{1}{4}

Simplify

= 3 x^{2}

\int_{0}^{4} 2 x^{3} + 1 d x

\int_{0}^{6} \frac{1}{1 + x ^{2}} d x

\int_{0}^{\frac{π}{6}} (sec (x) + tan (x))^{2} d x

\int_{1}^{2} \frac{ln ( x )}{x ^{10}} d x

\int_{2}^{3} \frac{1}{y - 3} d y

What is the integral from 0 to 1 of 12x^2y^3 ?
The integral from 0 to 1 of 12x^2y^3 is 3x^2