What is the integral from 0 to x of f(t) ?

The integral from 0 to x of f(t) is (x^2f)/2

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integral from 0 to x of f(t)

\int_{0}^{x} f (t) d t

\frac{x ^{2} f}{2}

Solution steps

\int_{0}^{x} f t d t

Take the constant out:

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

= f \cdot \int_{0}^{x} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{x}

= f [\frac{t ^{2}}{2}]_{0}^{x}

Compute the boundaries:

\frac{x ^{2}}{2}

= f \frac{x ^{2}}{2}

Simplify

= \frac{x ^{2} f}{2}

f (x) = \frac{3}{1 + x ^{2}}

\frac{\partial}{\partial x} (- \frac{2 y}{( 2 x + 3 y ) ^{2}})

y^{^{'}} = 2 y, y (0) = 1

\frac{d}{d x} (3 x^{2} x)

x \to 0 lim (\frac{5}{cos ( 5 x )})

What is the integral from 0 to x of f(t) ?
The integral from 0 to x of f(t) is (x^2f)/2