What is the integral from 2 to x of f(t) ?

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

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integral from 2 to x of f(t)

\int_{2}^{x} f (t) d t

f (\frac{x ^{2}}{2} - 2)

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

= f (\frac{x ^{2}}{2} - 2)

\int_{- 1}^{0} x^{2} e^{- 2 x} d x

\int_{0}^{2} (4 x^{2}) d x

\int_{2}^{\infty} \frac{2}{x ^{2}} d x

\int_{- 1}^{3} (3 x - x^{2}) d x

\int_{0}^{\frac{π}{2}} cos^{2} (3 t) d t

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