What is the integral from x to y of 1 ?

The integral from x to y of 1 is y-x

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integral from x to y of 1

\int_{x}^{y} 1 d x

y - x

Solution steps

\int_{x}^{y} 1 d x

Integral of a constant:

\int a d x = a x

= [1 \cdot x]_{x}^{y}

Simplify

= [x]_{x}^{y}

Compute the boundaries:

y - x

= y - x

\int_{1}^{3} \frac{2 x}{( x ^{2} + 4 ) ^{2}} d x

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

\int_{- 2}^{2} (x - 5) d x

\int_{5}^{10} \frac{6 x}{3 x ^{2} - 5} d x

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