What is the integral from x to x^2 of t^2 ?

The integral from x to x^2 of t^2 is (x^6-x^3)/3

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integral from x to x^2 of t^2

\int_{x}^{x^{2}} t^{2} d t

\frac{x ^{6} - x ^{3}}{3}

Solution steps

\int_{x}^{x^{2}} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{x}^{x^{2}}

= [\frac{t ^{3}}{3}]_{x}^{x^{2}}

Compute the boundaries:

\frac{x ^{6}}{3} - \frac{x ^{3}}{3}

= \frac{x ^{6}}{3} - \frac{x ^{3}}{3}

Simplify

= \frac{x ^{6} - x ^{3}}{3}

\frac{d y}{d x} 7 x + y = x - 6 x

\int \frac{e ^{x}}{1 + e ^{2 x}} d x

\frac{\partial}{\partial x} (\frac{x}{y + z})

\int x sin (4 x^{2}) d x

x \to - 2 lim (4 - 2 x)

What is the integral from x to x^2 of t^2 ?
The integral from x to x^2 of t^2 is (x^6-x^3)/3