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

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

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integral from x/2 to 2x-(x^2)/4 of 1

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

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

Solution steps

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

Integral of a constant:

\int a d x = a x

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

Simplify

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

Compute the boundaries:

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

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

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

\int_{0}^{s i n (x)} y d y

\int_{0}^{s i n (x)} x d x

\int_{0}^{x} cos (10 t) d t

\int_{0}^{6.8} 3 3 x + 4 d x

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