What is the integral from x^2 to 1 of 4x ?

The integral from x^2 to 1 of 4x is 2(-x^4+1)

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integral from x^2 to 1 of 4x

\int_{x^{2}}^{1} 4 x d x

2 (- x^{4} + 1)

Solution steps

\int_{x^{2}}^{1} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{x^{2}}^{1} x d x

Apply the Power Rule

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

Compute the boundaries:

\frac{1}{2} - \frac{x ^{4}}{2}

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

Simplify

= 2 (- x^{4} + 1)

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