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_{4}^{6} x^{2} + x - 9 d x

\int_{- 1}^{1} x^{2} + 3 d x

\int_{0}^{b} \frac{x}{x ^{2} + 1} d x

\int_{0}^{3} \frac{2 x + 3}{1 + x ^{2}} d x

\int_{2}^{3} \frac{2 x}{( x ^{2} + 4 ) ^{2}} d x

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)