What is the integral from 0 to 4 of 1/2 (sqrt(x))^2 ?

The integral from 0 to 4 of 1/2 (sqrt(x))^2 is 4

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integral from 0 to 4 of 1/2 (sqrt(x))^2

\int_{0}^{4} \frac{1}{2} (x)^{2} d x

4

Solution steps

\int_{0}^{4} \frac{1}{2} (x)^{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{4} (x)^{2} d x

Simplify

(x)^{2} : x

= \frac{1}{2} \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= \frac{1}{2} [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= \frac{1}{2} \cdot 8

Simplify

= 4

\int_{0}^{8} 462 e^{0.019 t} d t

\int_{0}^{10} x e^{(1 - x^{2})} d x

\int_{1}^{2} 4 π (t - 2)^{2} d t

\int_{3}^{5} 2 x^{2} - 2 d x

\int_{0}^{4} 2 x + 5 d x

What is the integral from 0 to 4 of 1/2 (sqrt(x))^2 ?
The integral from 0 to 4 of 1/2 (sqrt(x))^2 is 4