What is the integral from 1 to 2 of x(2x^2-1)^2 ?

The integral from 1 to 2 of x(2x^2-1)^2 is 57/2

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integral from 1 to 2 of x(2x^2-1)^2

\int_{1}^{2} x (2 x^{2} - 1)^{2} d x

\frac{57}{2}

Decimal

28.5

Solution steps

\int_{1}^{2} x (2 x^{2} - 1)^{2} d x

Apply u-substitution

: \int_{1}^{7} \frac{u ^{2}}{4} d u

= \int_{1}^{7} \frac{u ^{2}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{1}^{7} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{1}^{7}

= \frac{1}{4} [\frac{u ^{3}}{3}]_{1}^{7}

Compute the boundaries:

114

= \frac{1}{4} \cdot 114

Simplify

= \frac{57}{2}

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What is the integral from 1 to 2 of x(2x^2-1)^2 ?
The integral from 1 to 2 of x(2x^2-1)^2 is 57/2